It is 100 years since the well-known Mohr-Coulomb strength theory was established in 1900. A considerable amount of theoretical and experimental research on strength theory of materials under complex stress state was done in the 20th Century. This review article presents a survey of the advances in strength theory (yield criteria, failure criterion, etc) of materials (including metallic materials, rock, soil, concrete, ice, iron, polymers, energetic material, etc) under complex stress, discusses the relationship among various criteria, and gives a method of choosing a reasonable failure criterion for applications in research and engineering. Three series of strength theories, the unified yield criterion, the unified strength theory, and others are summarized. This review article contains 1163 references regarding the strength theories. This review also includes a brief discussion of the computational implementation of the strength theories and multi-axial fatigue.
Issue Section:
Review Articles
1.
Young
DH
(1972
), Stephen P Timoshenko 1878–1972
, Appl. Mech. Rev.
, 25
(7
), 759
–763
.2.
Timoshenko SP (1953), History of Strength of Materials, McGraw-Hill, New York, 1953.
3.
Timoshenko SP (1930), Strength of Materials Part 2, Advanced Theory and Problems, Third Ed, van Nostrand, Princeton, 1956.
4.
Mohr O (1905, 1913, 1928), Abhandlungen aus den Gebiete der Technischen Mechanik, Third Ed, Verlag von Wilhelm Ernst & Sohn, 1928.
5.
Westergaard
HM
(1920
), On the resistance of ductile materials to combined stresses
, J. Franklin Inst.
, 189
, 627
–640
.6.
Schleicher
F
(1925
), Z. Angew. Math. Mech.
, 5
, 199
199
.7.
Nadai
A
(1933
), ASME J. Appl. Mech.
, 1
, 111
–129
.8.
Nadai A (1950), Theory of Flow and Fracture of Solids, Vol. 1, McGraw-Hill, New York.
9.
Marin
J
(1935
), Failure theories of materials subjected to combined stresses
, Proc. Am. Soc. Civ. Eng.
, 61
, 851
–867
.10.
Gensamer M (1940), Strength of metals under combined stresses, ASM, 38–60.
11.
Meldahl A (1944), Brown Boveri Rev, Zurich, p. 260.
12.
Dorn JE (1948), Effect of stress state on the fracture strength of metals, In: Fracturing of Metals ASM, 32–50.
13.
Prager
W
(1949
), Recent developments in the mathematical theory of plasticity
, J. Appl. Phys.
, 20
, 235
–241
.14.
Freudental AM and Geiringer H (1958), In: Handbuch der Physik-Encyclopedia of Physics, Flu¨gge S (ed), Vol 6, The mathematical theories of the inelastic continuum, Elastizitat und Plastizitat, Springer, Berlin, 229–433.
15.
Naghdi PM (1960), Stress-strain relations in plasticity and thermo-plasticity, In: Plasticity, Lee EH and Symonds PS (eds), Pergamon Press, 121–169.
16.
Filonenko-Boroditch MM (1961), Mechanical Theories of Strength (in Russian), Moscow Univ Press, Moscow.
17.
Marin J (1962), Mechanical Behavior of Engineering Materials, Prentice-Hill, Englewood Cliffs.
18.
Paul B (1968), Macroscopic criteria for plastic flow and brittle fracture, In: Fracture, An Advanced Treatise, Vol 2, Liebowitz H (ed) Academic Press, New York, 313–496.
19.
Goldenblat II and Kopnov VA (1968), Yield and Strength Criteria for Structural Materials (in Russian), Machine Manufacturing Press, Moscow.
20.
Taira S et al. (1968), Strength of Metallic Materials at High Temperature: Theory and Design (Chinese Edition 1983), Science Press, Beijing.
21.
Tsai
SW
and Wu
EM
(1971
), A general theory of strength for anisotropic materials
, J. Compos. Mater.
, 5
(1
), 58
–80
.22.
Bell JF (1973), Mechanics of solids, Vol 1: The experimental foundations of solid mechanics, In: Encyclopedia of Physics, Vol 6a/1, Springer, Berlin, 483–512, 666–690.
23.
Krempl E (1974), The Influence of State of Stress on Low-cycle Fatigue of Structural Materials: A literature survey and interpretive report, ASTM STP 649, ASTM.
24.
Wu EM (1974), Phenomenological anisotropic failure criterion, Treatise on Composite Materials, Academic Press.
25.
Michino
MJ
and Findley
WN
(1976
), A historical perspective of yield surface investigation for metals
, Int. J. Non-Linear Mech.
, 11
(1
), 59
–82
.26.
Salencon J (1977), Applications of the Theory of Plasticity in Soil Mechanics, John Wiley & Sons, 158 pp.
27.
Geniev GA et al. (1978), Strength of Lightweight Concrete and Porous Concrete under Complex Stress State (in Russian), Moscow Building Press.
28.
Yu
MH
(1980
), Classical strength theories and its developments (in Chinese
), Mech. Pract.
, 2
(2
), 20
–25
.29.
Yu MH (1988), Three main series of yield and failure functions in plasticity, rock soil, and concrete mechanics (in Chinese), In: Researches on the Twin Shear Strength Theory, Xian Jiaotong Univ Press, 1–34.
30.
Zyczkowski M (1981), Combined Loadings in the Theory of Plasticity, Polish Scientific Publ, PWN, and Nijhoff.
31.
Chen WF (1982), Plasticity in Reinforced Concrete, McGraw-Hill, New York, 190–252.
32.
Ward IM (1983), Mechanical Properties of Polymers, Wiley-Int London.
33.
Chen WF and Baladi GY (1985), Soil plasticity: Theory and Imple-mentation, Elsevier, Amsterdam, 231 pp.
34.
Hamza H (1984), Critical strain energy as a failure and crack propagation criterion for ice, Proc IAHR Int Symp on Ice Prob.
35.
Shaw
MC
(1984
), A critical review of mechanical failure criteria
, ASME J. Eng. Mater. Technol.
, 106
, 219
–226
.36.
Hosford
WF
(1985
), Comments on anisotropic yield criterion
, Int. J. Mech. Sci.
, 27
, 423
423
.37.
Rowlands RE (1985), Strength (failure) theories and their experimental correlation, In: Failure Mechanics of Composites, Sih GC and Skudra AM (eds), Elsevier Science Pub., 71–125.
38.
Ikegami K and Niitsu Y (1989), Fundamental experiments on plastic deformation of stainless steel at high temperature, In: Advance in Constitutive Laws for Eng. Material, Int. Acad. Publ. 920–933.
39.
Desai
CS
(1989
), Single surface yield and potential function plasticity models: A review
, Computers and Geotechnics
, 7
, 319
–335
.40.
Klausner Y (1991), Fundamentals of Continuum Mechanics of Soils, Springer-Verlag, 437–485.
41.
Chen WF and Saleeb AF (1981, 1994), Constitutive Equations for Engineering Materials, Vol 1, Elasticity and Modelling; Vol 2, Plasticity and Modelling, Wiley, New York: Elasticity and modeling, Revised Edition, Elsevier, Amsterdam, 259–304, 462–489.
42.
Chen WF et al. (1994), Constitutive Equations for Engineering Materials, Vol 2: Plasticity and modeling, Elsevier, Amsterdam.
43.
Du QH (ed) (1994), An Encyclopedia of Engineering Mechanics, Higher Education Press, Beijing.
44.
Jiang JJ (1994), Non-linear Finite Element Analysis of Reinforced Concrete Structures (in Chinese), Xi’an: Shannxi Science and Technology Press, 15–34.
45.
Andreev GE (1995), Brittle Failure of Rock Materials: Test results and Constitutive Models, AA Balkema.
46.
Shen
ZJ
(1995
), Summary on the failure criteria and yield functions (in Chinese
), Chinese J. Geotech. Eng.
, 17
(2
), 1
–9
.47.
Kerr
AD
(1996
), Bearing capacity of floating ice covers subjected to static, moving, and oscillatory loads
, Appl. Mech. Rev.
, 49
(11
), 463
–476
.48.
Gao
H
and Brown
MW
(1996
), Multiaxial fatigue (in Chinese
), J. Mechanical Strength
, 18
(1
), 9
–13
.49.
You
BR
and Lee
SB
(1996
), A critical review on multiaxial fatigue assessments of metals
, Int. J. Fatigue
, 18
(4
), 235
–244
.50.
Sheorey PR (1997), Emperical Rock Failure Criterion, AA Balkema.
51.
Chen WF (1998), Concrete plasticity: Past, present and future, In: Strength Theory:Applications, Developments and Prospects for 21st Century, Yu MH and Fan SC (eds), Science Press, Beijing, New York, 7–48.
52.
Yu
MH
, Zhao
J
, and Guan
LW
(1998
), Strength theory for rock and concrete: History, present situation and development
, Prog. Nat. Sci.
, 8
(4
), 394
–402
.53.
Shen ZJ and Yu MH (1998), Summary on the failure criteria in deviatoric and meridian plane, In: Strength Theory: Applications, Developments and Prospects for 21st Century, Yu MH and Fan SC (eds), Science Press, Beijing, New York, 61–68.
54.
Munz D and Fett T (1999), Ceramics: Mechanical Properties, Failure Behaviour, Materials Selection, Springer Verlag, Berlin.
55.
Yu MH (1999), Engineering Strength Theory (in Chinese), Higher Education Press, Beijing.
56.
Yu MH (1992), New System of Strength Theory (in Chinese), Xian Jiaotong Univ Press, Xian.
57.
Coulomb CA (1773, 1776), Essai sur une application des regles de maximis et minimis a quelques problemes de statique, relatifs a l’architecture, Memoires de Mathematique et de Physique, presentes a l’ Academie, Royale des Sciences par divers Savans, et lus dans ses Assemblees, 7, 343–382, Paris (English translation: Note on an application of the rules of maximum and minimum to some statical problems, relevant to architecture, Heyman J., 1997, 41–74).
58.
Rankine WJM (1861), Manual of Applied Mechanics (1 edition, Ref. from Timoshenko, 1953, p 198; 21st edition, 1921).
59.
Mariotto E (1686), Traite du mouvement des eaux, (posthumously), de la Hire M ed; English transl by Desvaguliers JT, London (1718), 249.
60.
de
Saint-Venant
(1870
), Memoire sur l’establissement des equations differentielles des mouvements interieurs operes dans les corps solides ductiles au dela des limites ou l’e´lasticite´ pourrait les ramener a leur premier e´tat
, Comptes Rendus hebdomadaires des Seances de l’Academie des Sciences
, 70
, 473
–480
.61.
Tresca
H
(1864
), Sur I’ecoulement des corps solids soumis a de fortes pression
, Comptes Rendus hebdomadaires des Seances de l’Academie des Sciences, Rend
59
, 754
–758
.62.
Guest
JJ
(1900
), On the strength of ductile materials under combined stress
, Philos. Mag.
, 50
, 69
–133
.63.
Beltrami E (1885), Rend 1st Lombardo Sci. Lettere B18, 704–714.
64.
Foppl A (1900), Mitt Mech-tech Lab, Munch, T Ackermann, vol 7.
65.
Voigt
W
(1901
), Ann. Phys. (Leipzig)
, 4
(4
), 567
567
.66.
Nadai A (1931), Plasticity, McGraw-Hill, New York.
67.
Fromm H (1931), In: Handbuch der physikalischen und Technishchen Mechanik, vol 4, p. 359.
68.
Ros M and Eichinger A (1949), In: Die Bruchgefahrfester Korper, Bericht Nr. 172 der ENPA, Zurich.
69.
Mohr
O
(1882
), Uber die Darstellung des Spannungszustandes und des Deformationszustandes eines Korperelementes und uber die Anwendung derselben in der Festigkeitslehre
, Der Civlingenieur
, 28
, 113
–156
.70.
Mohr
O
(1900
), Welche Umstande bedingen die Elastizitatsgrenze und den Bruch eines Materials?
Zeitschrift des Vereins Deutscher Ingenieure Band
, 44
, 1524
–1530
.71.
von Karman
T
(1911
), Festigkeitsversuche unter allseitigem
, Z. Vereins Deutscher Ingenieure
, 55
, 1749
–1757
.72.
Boker
R
(1915
), Die Mechanik der bleibenden Formanderung in Kristallinisch aufgebauten Korpern
, Mitteilungen Forschungsarbeiten auf dem Gebiste Ingenieurwesens, Heft
, 175
, 1
–51
.73.
Haigh
BT
(1920
), The strain energy function and the elastic limit
, Engineering
, 109
, 158
–160
.74.
Burzynski W (1928), Studium and hipotezami wytezenia, Akad. Nauk Techn, Lwow.
75.
Naghdi
PM
and Trapp
JA
(1975
), On the nature of normality of plastic strain rate and convexity of yield surfaces in plasticity
, ASME J. Appl. Mech.
, 42
(1
), 61
–66
.76.
Yoder
RJ
and Iwan
WD
(1981
), On the formulation of strain-space plasticity with multiple loading surfaces
, ASME J. Appl. Mech.
, 48
(7
), 6
6
.77.
Yin
YQ
(1986
), Stress space and strain space formulation of the elasto-plastic constitutive relations for singular yield surface (in Chinese
), Acta Mech. Sin.
, 18
(1
), 31
–38
.78.
Marin J (1937), Prod. Eng. (N.Y.), May.
79.
Bazant ZP (1983) ed, Mechanics of Geomaterials: Rock, Concrete, Soil, Wiley-Interscience, New York.
80.
Drucker DC (1983), W Prager and his contributions, Mechanics of Geomaterials: Rock, Concrete, Soil, ZP Bazant (ed), Wiley-Interscience, New York.
81.
Drucker DC (1951), A more foundational approach to stress-strain relations, Proc. of 1st US-Natl Congress Appl. Mech., ASME 487–491.
82.
Edelman
F
and Drucker
DC
(1951
), Some extension of elementary plasticity theory
, J. Franklin Inst.
, 251
(6
), 581
–605
.83.
Bishop
JFW
and Hill
R
(1951
), A theory of the plastic distortion of a polycrystalline aggregate under combined stresses
, Philos. Mag.
, 42
, 414
–427
.84.
Davigenkov
NN
(1947
), In favour and against a uniform theory of strength (in Russian
), Bulletin Engineering and Technology
, 4
, 121
–129
.85.
Drucker
DC
(1953
), Limit analysis of two and three-dimensional soil mechanics problems
, J. Mech. Phys. Solids
, 1
, 217
–226
.86.
Volkov SD (1960), A Statistical Failure Theory (in Russian), Mashigiz, Moscow, 175 p.
87.
Hara Y (1966), The condition of slip in yielding, 15th Japan Congress of Applied Mechanics, 38–42.
88.
Hara Y (1971), On basic principles of the slip theory of plasticity, 20th Japan Congress of Applied Mechanics, 205–209.
89.
Shield
RT
(1955
), On Coulomb’s law of failure in soils
, J. Mech. Phys. Solids
, 4
(1
), 10
–16
.90.
Haythornthwaite
RM
(1961
), Range of yield condition in ideal plasticity
, J. Eng. Mech. Div.
, 87
(6
), 117
–133
.91.
Shibata T and Karube D (1965), Influence of the variation of the intermediate principal stress on the mechanical properties of normally consolidated clays, Proc. 6th Int. Conf. on Soil Mech. and Found Engrg., 1, 359–363, Univ of Toronto Press, Toronto.
92.
Mogi
K
(1967
), Effect of the intermediate principal stress on rock failure
, J. Geophys. Res.
, 72
, 5117
–5131
.93.
Mogi
K
(1971
), Fracture and flow of rocks under high triaxial compression
, J. Geophys. Res.
, 76
, 1255
–1269
.94.
Ko
HY
and Scott
RF
(1968
), Deformation of sand at failure
, J. Soil Mech. Found. Div.
, 94
(4
), 883
–898
.95.
Green
GE
and Bishop
AW
(1969
), A note on the drained strength of sand under generalized strain conditions
, Geotechnique
, 19
(1
), 144
–149
.96.
Vaid
YP
and Campanella
RG
(1974
), Triaxial and plane strain behaviour of natural clay
, J. Geotech. Eng.
, 100
(3
), 207
–224
.97.
Lade
PV
and Musente
HM
(1978
), Three-dimensional behavior of remolded clay
, J. Geotech. Eng.
, 104
(2
), 193
–208
.98.
Michelis
P
(1985
), Polyaxial yielding of granular rock
, J. Eng. Mech. Div.
, 111
(8
), 1049
–1066
.99.
Michelis
P
(1987
), True triaxial cycle behavior of concrete and rock in compression
, Int. J. Plast.
, 3
, 249
–270
.100.
Hoek
E
and Brown
ET
(1980
), Empirical strength criterion for rock masses
, J. Geotech. Eng.
, 106
(9
), 1013
–1035
.101.
Murrell
SAF
(1965
), The effect of triaxial stress system on the strength of rocks at atmospheric temperatures
, Geophys. J.
, 10
, 231
–282
.102.
Ashton
MD
, Cheng
DCH
, Farley
R
, and Valentin
FHH
(1965
), Rheol. Acta
, 4
, 206
206
.103.
Pramono
E
and Willam
K
(1989
), Implicit integration of composite yield surfaces with corners
, Eng. Comput.
, 6
, 186
–197
.104.
Pramono
E
and Willam
K
(1989
), Fracture energy-based plasticity formulation of plain concrete
, J. Eng. Mech. Div.
, 115
(6
), 1183
–1203
.105.
Bishop AW (1972), Shear strength parameters for undisturbed and remolded soil specimens, Stress Strain Behaviour of Soils, RHG Parry (ed), Foulis Co. Ltd, 1–59.
106.
Chen WF and Saleeb AF (1981), Constitutive Equations for Engineering Materials, Vol 1, Elasticity and Modelling; Vol 2, Plasticity and Modelling, Wiley, New York.
107.
Paul
B
(1961
), A modification of the Coulomb-Mohr theory of fracture
, ASME J. Appl. Mech.
, 28
(2
), 259
–268
.108.
Harkness RM (1971), An essay on Mohr-Coulomb, Stress-Strain Behaviour of Soils, RHG Parry (ed), Foulis Co., 212–219.
109.
Pankaj and Moin K (1991), Benchmark tests in Mohr-Coulomb elastoplasticity, Computational Mechanics, YK Cheung, HW Lee, and AYT Leung (eds), Balkema, Rotterdam, 753–759.
110.
Pankaj
and Moin
K
(1996
), Exact prescribed displacement field solutions in Mohr-Coulomb elastoplasticity
, Eng. Comput.
, 13
(1
), 4
–14
.111.
Heyman J (1997), Coulomb’s Menoir on Statics, Imperial College Press, London.
112.
Schajer
GS
(1998
), Mohr-Coulomb criterion expressed in terms of stress invariants
, ASME J. Appl. Mech.
, 65
, 1066
–1068
.113.
von Mises R (1913), Mechanik der festen Ko¨rper im plastisch deformablen Zustand, Nachrichten von der Ko¨niglichen Gesellschaft der wissenschaften zu Go¨ettinger, Mathematisch-physikalische Klasse, 582–592.
114.
Huber
MT
(1904
), Przyczynek do podstaw wytorymalosci
, Czasop Techn.
, 22
, 81
81
(Lwow, 1904); Pisma, 2, PWN, Warsaw, 1956.115.
Hencky H (1925), Zur Theorie plastischer Deformationen und der Hierdurch im Material hervogerufenen Nebenspannungen, Proc. 1st Int. Congr. on Appl. Mechanics, J Waltman, (ed) Delft, Technische Boekhandel en Druckerij.
116.
Novozhilov
VV
(1952
), On the physical meaning of stress invariants used in the theory of plasticity (in Russian
), Appl. Math. Mech.
, 16
(5
), 617
–619
.117.
Drucker
DC
and Prager
W
(1952
), Soil mechanics and plastic analysis for limit design
, Q. Appl. Math.
, 10
(2
), 157
–165
.118.
Humpheson C and Naylor DJ (1975), The importance of the form of the failure criterion, C/R/243/75, Swansea.
119.
Zienkiewicz OC and Pande GN (1977), Some useful forms of isotropic yield surfaces for soil and rock mechanics, Finite Elements in Geomechanics, G Gudehus (ed), John Wiley & Sons Ltd, 179–190.
120.
Willam KJ and Warnke EP (1975), Constitutive model for the triaxial behavior of concrete, Int. Assoc. Bridge. Struct. Eng. Proc., 19 1–31.
121.
Matsuoka H and Nakai T (1974), Stress-deformation and strength characteristics of soil under three different principal stresses, Proc. of Japan Society of Civil Engineers, 232, 59–70.
122.
Lade
PV
and Duncan
JM
(1975
), Elastoplastic stress-strain theory for cohesionless soil
, J. Geotech. Eng.
, 101
(10
), 1037
–1053
.123.
Ottosen
NS
(1977
), A failure citerion for concrete
, J. Eng. Mech.
, 103
(4
), 527
–535
.124.
Lade
PV
(1977
), Elasto-plastic stress strain theory for cohesionless soil with curved yield surface
, Int. J. Solids Struct.
, 13
(11
), 1019
–1035
.125.
Kotsovos
MD
(1979
), A mathematical description of the strength properties of concrete under generalized stress
, Mag. Concrete Res.
, 31
(108
), 151
–158
.126.
Argyris JH, Faust G, Szimmat J, Warnke EP, and Willam KJ (1973), Recent developments in the finite element analysis of prestressed concrete reactor vessels, Proc of 2nd Int Conf SMIRT, Berlin.
127.
Gudehus G (1972), Elasto-plastic constitutive equations for dry sand, Archives of Mechanics, 24(3), 395–402.
128.
Gudehus
G
(1973
), Elastoplasticher Stoffgleichungen fur trockenn Sand
, Ingeniur Archiv.
, 42
, 151
–169
.129.
Lin
FB
and Bazant
ZP
(1986
), Convexity of smooth yield surface of frictional material
, J. Eng. Mech. Div.
, 112
(11
), 1259
–1262
.130.
Shi
SZ
and Yang
GH
(1987
), An improvement of the commonly used yield function for rock material
, Chinese J. Geotech. Eng.
, 9
(2
), 60
–69
.131.
Yu
MH
and Liu
FY
(1990
), Smooth ridge model of generalized twin shear stress criterion (in Chinese
), Acta Mech. Sin.
, 22
(2
), 213
–216
.132.
Podgorski
J
(1985
), General failure criterion for concrete
, J. Eng. Mech. Div.
, 111
(2
), 188
–201
.133.
Menetrey
P
and Willam
KJ
(1995
), Triaxial failure criterion for concrete and its generalization
, Colloid J. USSR
, 92
(3
), 311
–318
.134.
Krenk
S
(1996
), Family of invariant stress surface
, J. Eng. Mech.
, 122
(3
), 201
–208
.135.
Shen ZJ (1989), A stress-strain model for sands under complex loading, Advance in Constitutive Laws for Eng. Mater., Int. Acade. Publ., 303–308.
136.
Yin
GZ
, Li
H
et al. (1987
), The experimental study of the influence of engineering stress changes on strength characteristics of rocks
, Chinese J. Geotech. Eng.
, 9
(2
), 20
–28
(English abstract).137.
Wang
CZ
, Guo
ZH
, and Zhang
XQ
(1987
), Experimental investigation of biaxial and triaxial compressive concrete strength
, ACI Mater. J.
, 84
(2
), 92
–100
.138.
Guo
ZH
and Wang
CZ
(1991
), Investigation of strength and failure criterion of concrete under multi-axial stresses (in Chinese
), China Civil Engineering Journal
, 24
(3
), 1
–14
.139.
Zhang
YG
and Hwang
KC
(1990
), Acta Mechanica Solida Sinica
, 12
(3
), 277
–285
.140.
Jiang JJ and Wang HL (1998), Five-parameter failure criterion of concrete and its application, Strength Theory, Science Press, Beijing, New York, 403–408.
141.
Song
YB
, Zhao
GF
et al. (1991
), Deformation and strength of concrete under tri-axial loading (in Chinese
), J. Hydraul. Eng.
, 38
(12
), 10
–16
.142.
Song
YP
and Zhao
GF
(1996
), A general failure criterion for concretes under multi-axial stress
, China Civil Eng. Journal
, 29
(2
), 25
–32
.143.
Tokuoka
T
(1971
), Yield conditions and flow rules derived from hypo-elasticity
, Arch. Ration. Mech. Anal.
, 42
(4
), 239
–252
.144.
Lee
YK
and Ghosh
J
(1996
), The significance of J3 to the prediction of shear bands
, Int. J. Plast.
, 12
(9
), 1179
–1197
.145.
Hu
GK
Schmit
F
, Baptise
D
, and Francois
D
(1996
), Visco-plastic analysis of adhesive joints
, J. Eng. Mech. Div.
, 63
(1
), 21
21
.146.
Hashiguchi
K
(1973
), Theories of the yield for frictional materials
, Trans. Japan Society of Civil Engineers
, 4
, 144
–145
.147.
Maitra
M
Majumdar
K
, and Das
A
(1973
), Unified plastic yield criterion for ductile solids
, AIAA J.
, 11
(10
), 1428
–1429
.148.
Haddow
JB
and Hrudey
TM
(1971
), The yield condition and flow rule for a metal subjected to finite elastic volume change
, ASME J. Basic Eng.
, D93
(4
), 708
–712
.149.
Parry RHG (ed), (1972), Stress-Strain Behaviour of Soils, (Proc. of the Roscoe Memorial Symp., Cambridge Univ, 1971), GT Foulis & Co Ltd Oxford.
150.
Wood DM (1990), Soil Behaviour and Critical State Soil Mechanics, Cambridge Univ Press, New York.
151.
Yu MH (1961), General behaviour of isotropic yield function (in Chinese), Res Report of Xi’an Jiaotong Univ, Xi’an.
152.
Yu MH (1961), Plastic potential and flow rules associated singular yield criterion (in Chinese), Res. Report of Xi’an Jiaotong Univ, Xi’an.
153.
Yu
MH
(1983
), Twin shear stress yield criterion, Int. J. of Mech. Sci.
, 25
(1
), 71
–74
.154.
Yu MH (1962), Brittle fracture and plastic yield criterion (in Chinese) Res Report of Xi’an Jiaotong Univ, Xi’an.
155.
Yu
MH
, He
LN
, and Song
LY
(1985
), Twin shear stress theory and its generalization
, Sci. Sin., Ser. A
, English edition, 28
(11
), 1174
–1183
.156.
Yu MH (1998), Twin Shear Theory and its Application (in Chinese), Science Press, Beijing, 834 pp.
157.
Yu
MH
and He
LN
(1983
), Non-Schmid effect and twin shear stress criterion of plastic deformation in crystals and polycrystalline metals (English Abstract
), Acta Metall. Sin.
, 19
(5
), 190
–196
.158.
Yu
MH
and Liu
FY
(1988
), Twin shear three-parameter criterion and its smooth ridge model (English Abstract
), China Civil Engng. J.
, 21
(3
), 90
–95
.159.
Yu
MH
and Liu
FY
et al. (1990
), A new general strength theory (English Abstract
), China Civil Engrg. Journal
, 23
(1
), 34
–40
.160.
Yu MH and Li YM (1987), Generalized shear stress bi-elliptical cap model, Proc. of 6th China Conf. of Soil Mech. and Found. Eng., China Civil Eng Press, Beijing, 165–169.
161.
Li XC, Xu DJ, Liu SH, and An M (1994), The experimental research of the strength, deformation and failure properties of Laxiwa granite under the status of true triaxial stresses, Proc of 3rd Conf of Chinese Soc for Rock Mechanics and Engineering, China Sci. and Tech. Press, 153–159.
162.
Ming
YQ
, Sen
J
, and Gu
JS
(1994
), Tension-compression true triaxial test facility and its application (in Chinese
), Protecting Eng.
, 3
, 1
–9
.163.
Launay P and Gachon H (1972), Strain and ultimate strength of concrete under triaxial stress, Am Concrete Inst Spec Publ 34, Paper No 13, 269–282.
164.
Lu
CS
(1995
), Application of the generalized twin shear stress strength theory to concrete under true triaxial compressive state (in Chinese
), J of Xian Jiaotong Univ.
, 29
(8
), 95
–101
.165.
Lu
CS
(1995
), Method of application of the generalized twin shear strength theory, (in Chinese
), China Civil Engineering Journal
, 28
(4
), 73
–77
.166.
Wang
ZS
, Li
YM
, and Yu
MH
(1990
), Twin shear stress criterion applied to rock strength, (in Chinese
), Chinese J. Geotech. Eng.
, 12
(4
), 68
–72
.167.
Winstone MR (1984), Influence of prestress on the yield surface of the cast nickel superalloy Mar-M002 at elevated temperature, Mechanical Behavour of Materials-4 (ICM-4), 1, J Carlsson and NG Ohlson (eds), Pergamon Press, 199–205.
168.
Yu MH, Liu JY et al. (1994), Twin-shear slip line field, Proc of 1st Asia-Oceania Int Symp on Plasticity, TC Wang and BY Xu (eds), Peking Univ Press, Beijing, 432–437.
169.
Yan ZD and Bu XM (1993), The method of characteristics for solving the plane stress problem of ideal rigid-plastic body on the basis of Twin shear stress yield criterion, Advances in Engineering Plasticity and its Applications, WB Lee (ed), Elsevier, 295–302.
170.
Yan
ZD
and Bu
XM
(1993
), The method of characteristics for solving the plane stress problem of ideal rigid-plastic body on the basis of three yield criteria, (in Chinese
), Eng. Mechanics
, (Suppl), 10
, 89
–96
.171.
Yan
ZD
and Bu
XM
(1996
), An effective characteristics method for plastic plane stress problem
, J. Eng. Mech.
, 122
(6
), 502
–506
.172.
Zhao
DW
, Zhao
ZY
, and Zhang
Q
(1991
), Solving compression of an annulus by Twin shear stress criterion (in Chinese
), Eng. Mech.
, 8
(2
), 75
–80
.173.
Zhao
DW
, Zhao
ZY
, and Zhang
Q
(1991
), Solving compression of a shallow plate by the Twin shear stress criterion, (English Abstract), (in Chinese
), J Northeast Univ. of Tech.
, 12
(1
), 54
–58
.174.
Zhao
DW
and Wang
GD
(1993
), Analytic solution to hot extension forging of rounds based on Twin-shearing stress criterion
, J. Northeast Univ. of Tech.
, 14
(4
), 377
–382
.175.
Zhao
DW
, Li
GF
, and Liu
FL
(1994
), The surface integral to the axisymmetric rod drawing through the elliptic-die profile (by use of the twin shear strength theory, in Chinese
), Eng. Mech.
, 11
(4
), 131
–136
.176.
Zhao DW, Xu JZ, Yang H, Liu XH, and Wang GD (1998), Application of twin shear stress yield criterion in Axisymmetric indentation of a semiinfinite medium, Strength Theory, Science Press, Beijing, 1079–1084.
177.
Li
YM
(1988
), Elastoplastic limit anlysis with a new yield criterion (twin-shear yield criterion, in Chinese
), J. Mech. Strength
, 10
(3
), 70
–74
.178.
Huang
WB
and Zeng
GP
(1989
), Solving some plastic problems by using the Twin Shear Stress criterion (in Chinese
), Acta Mech.
, 21
(2
), 249
–256
.179.
Chen
JJ
(1996
), The determination of the limit load of an axisymmetric shallow spherical shell by use of the Twin shear stress yield criterion (in Chinese
), Shanghai J. Mech.
, 17
(2
), 159
–162
.180.
Wang
ZX
(1997
), Determination of limit loads of thick wall cylinder with Twin Shear Strength theory (in Chinese
), J. Jiangsu Univ. of Sci. and Tech.
, 18
(2
), 81
–84
.181.
An
M
, Yu
MH
, and Wu
X
(1991
), Applications of generalized twin shear yield criterion in rock mechanics (in Chinese
), Rock Soil Mech
, 12
(1
), 17
–26
.182.
Quint Co (1993), COMPMAT–Analysis system for composite materials, FEM codes of Quint Corp, Japan.
183.
Quint Co (1994), PREMAT/POSTMAT - Pre and post processor for composite materials, FEM codes of Quint Corp, Japan.
184.
Quint Co (1994), STAMPS-Structural analysis program for civil engineering. EM codes of Quint Corp, Japan.
185.
Li YM, Ishii K, Nakazato C, and Shigeta T (1994), Prediction of safety rate and multi-slip direction of slip failure under complex stress state, Advances Engng. Plasticity and its Applications, BY Xu and W Yang (eds), Int Acad Pub, 349–354.
186.
Luo ZR and Li ZD (1994), Progressive failure of geomaterial thick cylinder (by using of the twin shear strength theory of Yu), Proc of 7th China Conf on Soil Mech and Found Eng, China Civil Engrg Press, Xian, 200–203.
187.
Li YM and Ishii KZ (1998), The evaluation of strength for the composite materials, Strength Theory, Science Press, Beijing, New York, 337–342.
188.
Liu
F
, Li
LY
, and Mei
ZX
(1994
), Elasto-visco-plastic finite element analysis of self-enhanced thick cylinder (in Chinese
), Chin J Appl Mech
, 11
(3
), 133
–137
.189.
Zhang XY (1993), Plasticity for Geomaterials (in Chinese), Transportation Press, Beijing, 91–135.
190.
Zhu
FS
(1997
), Strength criteria and constitutive model for rock and rock masses (in Chinese
), Mechanics and Practics
, 19
(5
), 8
–14
.191.
Li JC and Zhang YQ (1998), Limit analysis of a wellbore based on the twin-shear strength theory, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 1103–1108.
192.
Liu XQ, Ni XH, Yan S et al. (1998), Application of the twin shear strength theory in strength-calculation of gun barrels, Strength Theory: Applications, Developments, and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 1039–1042.
193.
Yan
ZD
(1996
), Solution of the axisymmetrical punching problem of concrete slab by the Twin shear strength theory (in Chinese
), Eng Mech
, 13
(1
), 1
–7
.194.
Liao HJ and Yu MH (1998), Application of twin shear strength theory in soil liquefaction, Strength Theory, Science Press, Beijing, New York, 245–252.
195.
Chen JJ (1998), The determination of the limit load of a square plane by twin shear stress yield criterion, Strength Theory, Science Press, Beijing, New York, 1009–1014.
196.
Chen
ZP
(1998
), Nonlinear stress analysis of arch dam (in Chinese
), Eng Mech
, 15
(4
), 62
–73
.197.
Chen ZP and Chen SH (1998), The ice load on cone, Strength Theory, Science Press, Beijing, 1085–1090.
198.
Ni XH, Liu XQ et al. (1998), Calculation of stable loads of strength differential thick cylinders and spheres by the twin shear strength theory, Strength Theory, Science Press, Beijing, New York, 1043–1046.
199.
Zhuang
JH
and Wang
WY
(2000
), Limit analysis of the infinite plate containing a circular hole under uniform pressure with different strength in tension and compression (in Chinese
), J. Appl. Mech.
, 17
(2
), 70
–74
.200.
Scoble
WA
(1906
), The strength and behavior of ductile materials under combined stress
, Philos. Mag.
, 12
, 533
–547
.201.
Scoble
WA
(1910
), Ductile materials under combined stress
, Philos. Mag.
, 16
, 116
–128
.202.
Smith
CA
(1909
), Some experiments on solid steel bars under combined stress
, Engineering
, 20
, 238
–243
.203.
Lode
W
(1926
), Versuche ueber den Einfluss der mittleren Hauptspannung auf das fliessen der metals eisen kupfer und nickel
, Z. Phys.
, 36
, 913
–939
.204.
Taylor
GI
and Quinney
H
(1931
), The plastic distortion of metals
, Philos. Trans. R. Soc. London, Ser. A
, 230
, 323
–362
.205.
Ivey
HJ
(1961
), Plastic stress-strain relations and yield surfaces for aluminium alloys
, J. Mech. Eng. Sci.
, 3
(1
), 15
–31
.206.
Pisarenko GS and Lebedev AA (1976), Deformation and Strength of Material Under Complex Stressed State (in Russian), Naukova Dumka, Kiev.
207.
Cook
G
and Robertson
A
(1911
), The strength of thick hollow cylinders under internal pressure
, Engineering
, 92
, 786
–789
.208.
Guest
JJ
(1940
), Yield surface in combined stress
, Philos. Mag.
, 30
, 349
–369
.209.
Lessells
JM
and MacGregor
CW
(1940
), Combined stress experimentals on a Nickel-Chrome-Molybdenum steel
, J. Franklin Inst.
, 230
, 163
–181
.210.
Davis
EA
(1943
), Increase of stress with permanent strain and stress-strain relations in the plastic state for copper under combined stresses
, ASME J. Appl. Mech.
, 10
(2
), 187
–196
.211.
Davis
EA
(1945
), Yielding and fracture of medium-carbon steel under combined stress
, ASME J. Appl. Mech.
, 12
(1
), 13
–24
.212.
Nadai
A
(1947
), The flow of metals under various stress conditions
, Proc. Inst. Mech. Eng.
, 157
, 121
–160
.213.
Osgood
WR
(1947
), Combined-stress tests on 24S-T Aluminium alloy tubes
, ASME J. Appl. Mech.
, 14
, 247
–253
.214.
Morrison
JLM
(1948
), The criterion on yield of gun steels
, Proc. Inst. Civ. Eng., Struct. Build.
, 159
, 81
–94
.215.
Gough
HJ
(1949
), Engineering steel under combined cyclic and static stress
, Proc. Inst. Mech. Eng.
, 60
, 417
–440
.216.
Morrison
JLM
and Shepherd
WM
(1950
), An experimental investigation of plastic stress-strain relations
, Proc. Inst. Mech. Eng.
, 173
, 1
–19
.217.
Marin
J
et al. (1953
), Plastic stress-strain relations for biaxial tension and non-radial combined stress loading
, J. Franklin Inst.
, 256
(2
), 119
–128
.218.
Marin
J
and Hu
LW
(1956
), Biaxial plastic stress-strain relations of a mild steel for variable stress ratios
, ASME Trans.
, 78
, 499
499
.219.
Naghdi
PM
, Essenburg
F
, and Koff
W
(1958
), An experimental study of initial and subsequent yield surfaces in plasticity
, ASME J. Appl. Mech.
, 25
(2
), 201
–209
.220.
Ratner SI (1949), Strength and Plasticity, National Defence Press, Moscow.
221.
Zhang
ZH
and Pan
PJ
(1996
), Experimental research on the yield and strength of magnesium alloy under complex stress condition
(in Chinese), Acta Mech Solida Sinica
, 17
(2
), 163
–166
.222.
Ishlinsky A Yu (1940), Hypothesis of strength of shape change (in Russian), Uchebnye Zapiski Moskovskogo Universiteta, Mekhanika, 46.
223.
Hill
R
(1950
), Philos. Mag.
, 41
, 733
–744
.224.
Bridgman
PW
(1923
), The compressibility of thirty metals as a function of pressure and temperature
, Proc. Am. Acad. Arts Sci.
, 58
, 163
–242
.225.
Bridgman
PW
(1947
), The effect of hydrostatic pressure on the fracture of brittle substances
, J. Appl. Phys.
, 18
, 246
246
.226.
Bridgman PW (1952), Studies in Large Plastic Flow and Fracture with Special Emphasis on the Effects of Hydrostatic Pressure, McGraw-Hill, New York.
227.
Bridgman PW (1964), Studies in Large Plastic Flow and Fracture, Cambridge, Harvard Univ Press.
228.
Bridgman PW (1964), Collected Experimental Papers, Harvard Univ Press, Cambridge, Vol 1 (Papers 1–11) to Vol 7 (Papers 169–199).
229.
Richart FE, Brandtzaeg A, and Brown RL (1928), A study of the failure of concrete under combined compressive stresses, Univ Illinois Exp St Bull No 185.
230.
Balmer GG (1949), Shearing strength of concrete under high triaxial stress-computation of Mohr’s envelope as a curve, Struct Res Lab Report, SP-23 Denver.
231.
Hu
LW
(1956
), An experimental study of the fracture of metals under hydrostatic pressure
, J. Mech. Phys. Solids
, 4
(2
), 96
–103
.232.
Hu LW (1960), Stress-strain relations and hydrostatic stress, Plasticity, EH Lee and PS Symonds (eds), Pergamon Press, Oxford, 194–201.
233.
Prager
W
(1945
), Strain hardening under combined stress
, J. Appl. Phys.
, 16
, 837
–840
.234.
Hencky
HZ
(1924
), Zur Theorie plastischer Deformationen und hierdurch in Material hervorgenrufenen Nachhspannungen
, Z. Angew. Math. Mech.
, 4
, 323
–334
.235.
Geiringer H (1930), Beit zum Vollstandigen ebenen Olastizitats problem, Proc. 3rd Int Congress Appl Mech 2, 185–190.
236.
Prandtl L (1920), Uber die Harte Plastischer Koerper, Goettinger nachr, Math Phys Kl, 74–85.
237.
Prandtl
L
(1923
), Anwendungabeispiele zu einem henchyschen Satz ueber das Plastische Gleichgewicht
, Z. Angew. Math. Mech.
, 3
, 468
468
.238.
Prandtl L (1925), Spannungsverteilung in plastischen Koerper n, Proc of 1st Int Congress on Applied Mechanics, Delft Technische Boekhandel en Druckerij, J Waltman Jr (ed), 43–54.
239.
Prager W (1953), A geometrical discussion of the slip-line field in plane plastic flow, Trans. Roy. Inst. Tech. (Stockholm), 65, 1–26.
240.
Prager W (1955), The theory of plasticity: a survey of recent achievements, Proc of the Inst of Mech Eng, 169, 41–57.
241.
Johnson W, Sowerby I, and Venter RD (1982), Plane-Strain Slip Line Fields for Metal Deformation Processes–A Source Book and Bibliography, Pergamon Press.
242.
Kachanov LM (1971), Foundations of the Theory of Plasticity, Series of “Applied Mathematics and Mechanics,” HA Lauwerier and WT Koiten (eds), 12, North-Holland Pub, Amsterdam.
243.
Hill R (1950), The Mathematical Theory of Plasticity, Clarendon Press, Oxford.
244.
Haar A and von Karman T (1909), Zur Theorie der Spanungszustande in plastischen und sandartigen Med. Nachr. Gesellsch. Wissensch., Gottingen, Math-phys. Klasse, 204.
245.
Sokolovski VV (1946), Theory of Plasticity (in Russian), Moscow.
246.
Onkcov (1963), Engineering Plasticity (Chinese translation from Russian), Science Press, Beijing.
247.
Thomsen EG, Yang CT, and Kobayash S (1965), Mechanics of Plastic Deformation in Metal Processing, MacMillan.
248.
Gurson
AL
(1977
), Continuum theory of ductile rupture by void nucleation and growth: Part one-Yield criterion and flow rules for porous ductile media
, J. Eng. Mater. Technol.
, 99
, 2
–15
.249.
Gurson AL (1977), Porous rigid-plastic materials containing rigid inclusions yield function, plastic potential and void nucleations, ICF4 2A, 357.
250.
Tvergaard
V
(1981
), Influence of voids on shear band instabilities under plane strain conditions
, Int. J. Fract.
, 17
, 389
–407
.251.
Tvergaard
V
(1982
), On localization in ductile materials containing spherical voids
, Int. J. Fract.
, 18
, 237
–252
.252.
Tvergaard
V
(1987
), Effect of yield surface curvation and void nucleation on plastic flow localization
, J. Mech. Phys. Solids
, 35
, 43
–60
.253.
Gologanu M, Leblond JB et al. (1997), Recent extensions of Gurson’s model for porous ductile metals, Continuum Micromechanics, P Suquet (ed), Springer, Wien, 61–130.
254.
Drucker
DC
, Prager
W
, and Greenberg
HJ
(1952
), Extended limit design theorems for continuous media
, Q. Appl. Math.
, 9
, 381
–389
.255.
Drucker
DC
(1954
), Limit analysis and design
, Appl. Mech. Rev.
, 7
(10
), 421
–423
.256.
Hodge PG (1959), Plastic Analysis of Structures, McGraw-Hill New York.
257.
Save MA and Massonnet CE (1972), Plastic Analysis and Design of Plates Shells, and Disks. North-Holland.
258.
Brebbia CA (ed), (1985), Finite Element Systems, Springer-Verlag, Berlin.
259.
Hershey
AV
(1954
), The plasticity of an isotropic aggregate of anisotropic face-centered cubic crystals
, ASME J. Appl. Mech.
, 21
(3
), 241
–249
.1.
Bailey
RW
(1935
), The utilization of creep test in engineering design
, J. Inst. Mech. Eng. London
131
, 186
–205
, 2.
(
1935
), 131
, 260
–265
.1.
Davis
EA
(1961
), The Bailey flow rule and associated yield surface
, ASME J. Appl. Mech.
, 28
(1
), 310
310
.2.
Hosford
Jr WF
(1972
), A generalized isotropic yield creterion
, ASME J. Appl. Mech.
, E39
(2
), 607
–609
.3.
Barlat
F
and Lian
J
(1989
), Plastic behavior and stretchability of sheet metals, Part One: A yield function for orthotropic sheets under plane strain condition
, Int. J. Plast.
, 5
, 51
–56
.4.
Owen DRJ and Peric D (1992), Recent developments in the application of finite element methods to nonlinear problems, Computationnal Methods in Engineering: Advances & Applications, AAO Tay and KY Lam (eds), Singapore, World Scientific, 3–14.
5.
Tan
JJ
(1990
), Unified form of yield criteria for metallic materials
, Chin. Sci. Bull.
, 35
(7
), 555
–557
.6.
Karafillis
AP
and Boyce
MC
(1993
), A general anisotropic criterion using bounds and a transformation weight tensor
, J. Mech. Phys. Solids
, 41
(12
), 1859
–1886
.7.
Dodd
B
and Naruse
K
(1989
), Limitation on isotropic yield criterion
, Int. J. Mech. Sci.
, 31
(7
), 511
–519
.8.
Hill
R
(1993
), A user-friendly theory of orthotropic plasticity in sheet metals
, Int. J. Mech. Sci.
, 35
, 19
19
.9.
Barlat
F
, Becker
C
, Hayashida
Y
et al. (1997
), Yielding description for solution strengthened aluminum alloys
, Int. J. Plast.
, 13
(4
), 385
–401
.10.
Barlat
F
, Meada
Y
, Chung
K
et al. (1997
), Yield function development for aluminum alloys sheets
, J. Mech. Phys. Solids
, 45
(11/12
), 1727
–1763
.11.
Yu MH and He LN (1991), A new model and theory on yield and failure of materials under the complex stress state, Mechanical Behaviour of Materials-6. (ICM-6), M Jono and T Inoue (eds), Pergamon Press, Oxford, 3, 841–846.
12.
Yu
MH
, He
LN
, and Liu
CY
(1992
), Generalized twin shear stress yield criterion and its generalization
, Chin. Sci. Bull.
, 37
(24
), 2085
–2089
.13.
Yu MH (2002), Unified Strength Theory and Applications, Springer, Berlin.
14.
Yu MH, He LN, and Zeng WB (1992), A new unified yield function: Its model, computational implementation and engineering application, Computationnal Methods in Engineering: Advances & Applications, AA Tay and KY Lam (eds), World Scientific, 157–162.
15.
Wang
SJ
and Dixon
MW
(1997
), New static failure criterion for ductile materials
, J. Strain Anal. Eng. Des.
, 32
(5
), 345
–350
.16.
Ma
GW
and He
LN
(1994
), Unified solution to plastic limit of a simply supported circular plate (in Chinese
), Mech. Pract.
, 16
(6
), 46
–48
.17.
Ma GW, Yu MH, Iwasaki S et al. (1994), Plastic analysis of circular plate on the basis of the unified yield criterion, Proc. of Int. Conf. on Comput. Methods in Structural and Geotech. Eng., PKK Lee, LG Tham, and YK Cheung (eds), China Transl & Print Ltd, Hong Kong, 3, 930–935.
18.
Ma
GW
, Yu
MH
, Miyamoto
Y
, Wasaki
S
(1995
), Unified plastic solution to circular plate under portion uniform load
, J. Struct. Eng. (Japan)
41A
, 385
–392
.19.
Ma
GW
, Yu
MH
, Iwasaki
S
, and Miyamoto
Y
(1995
), Unified elasto-plastic solution to rotating disc and cylinder
, J. Struct. Eng.
41A
, 79
–85
.20.
Zhao
JH
(1998
), The limit load of rectangular plate by use of the unified yield criterion (in Chinese
), J. Mech. Strength
20
(3
), 181
–184
.21.
Li
JC
, Yu
MH
, and Xiao
Y
(2000
), Unified limit solution for oblique plate of metal (English Abstract
), Chinese J. of Mech. Engrg.
36
(8
), 25
–28
.22.
Ma
GW
, Hao
H
, and Miyamoto
Y
(2001
), Limit angular velocity of rotating disc with unified yield criterion
, Int. J. Mech. Sci.
, 43
, 1137
–1153
.23.
Guowei
M
, Iwasaki
S
, and Miyamoto
Y
(1998
), Plastic limit analyses of circular plates with respect to unified yield criterion
, Int. J. Mech. Sci.
, 40
(10
), 963
–976
.24.
Ma
G
, Hao
H
, and Iwasaki
S
(1999
), Unified plastic limit analysis of circular plates under arbitrary load
, ASME J. Appl. Mech.
, 66
(6
), 568
–570
.25.
Ma
G
, Hao
H
, and Iwasaki
S
(1999
), Plastic limit analysis of a clamped circular plates with unified yield criterion
, Struct Eng Mech
7
(5
), 513
–525
.26.
Ma
G
, Iwasaki
S
, and Miyamoto
Y
(1999
), Dynamic plastic behavior of circular plate using unified yield criterion
, Int. J. Solids Struct.
, 36
(3
), 3257
–3275
.27.
Qiang HF, Xu YH, Zhu JH et al. (1998), Unified solutions of crack tip plastic zone under small scale yielding, Strength Theory: Applications, Developments, and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 823–829.
28.
Foppl A and Foppl L (1924), Drang und Zqang, Munich, second edition, 1, p. 50.
29.
Ros M and Eichinger A (1926), Versuche sur Klarung der Frage der Bruchgefahr, Proc of 2nd Int Congress of Applied Mechanics, Zurich, 315–327.
30.
Reuss
E
(1930
), Beruecksichtigung der elastischen Formaenderungen in der Plastizitaetstheorie
, Z. Angew. Math. Mech.
, 10
, 266
–274
.31.
Hill
R
(1952
), On discontinuous plastic state
, J. Mech. Phys. Solids
, 1
(1
), 19
–30
.32.
Koiter
WT
(1953
), Stress-strain relations, uniqueness and variational theorem for elastic-plastic material with a singlar yield surface
, Q. Appl. Math.
, 11
(3
), 29
–53
.33.
Prager
W
(1953
), On the use of singular yield conditions and associated flow rules
, ASME J. Appl. Mech.
, 20
, 317
–320
.34.
Hodge
Jr PG
(1957
), A general theory of piecewise linear isotropic plasticity based on maximum shear
, J. Mech. Phys. Solids
, 5
, 242
–260
.1.
Thomas
TY
(1957
), Extended compatibility conditions for the study of surfaces of discontinuity in continuum mechanics
, J. Math. Mech.
, 6
, 311
–322
, 2.
6
, 907
–908
.1.
Naghdi
PM
, Rowley
JC
, and Beadle
CW
(1955
), Experiments concerning the yield surface and the assumption of linearity in the plastic stress-strain relations
, ASME J. Appl. Mech.
, 22
, 416
–420
.2.
Prager W (1955), Discontinuous fields of plastic stress and flow, Proc. of 2nd US Natl. Congress of Appl. Mech., 21–32.
3.
Siebel E and Maier A (1933), Der einfluss mechrachsiger Spannungazustande auf das Formanderungsvermogen metallischer Werkstoffe, Zeit, VDI 77, 1345–1349.
4.
Phillips A (1960), Pointed Vertices in plasticity, Plasticity, EH Lee and PS Symonds (ed), Pergamon Press, Oxford, 202–214.
5.
Shield
R
and Ziegler
H
(1958
), On Prager’s hardening rule
, Z. Angew. Math. Phys.
, 9a
, 260
–276
.6.
Il’yushin
AA
and Lensky
VS
(1959
), On the laws of deformation of materials under combined loading (in Chinese
), Acta Mech.
, 3
, 3
3
.7.
Il’yushin
AA
(1960
), On the increments of plastic deformation and the yield surface (in Russian
), PMM
, 24
, 663
–667
.8.
Ivlev
DD
(1959
), On the relations describing plastic flow for the Tresca yield condition and its generalizations (in Russian
), Report Sci. Acad. USSR
124
(3
), 546
–549
.9.
Ziegler
H
(1959
), A modification of Prager’s hardening rule
, Q. Appl. Math.
, 17
(1
), 55
–65
.10.
Hill
R
(1961
), Discontinuity relations in mechanics of solids
, Prog Solid Mech
2
, 247
–276
.11.
Il’yushin
AA
(1961
), On the postulate of plasticity
(in Russian), PMM
25
(3
), 503
–507
.12.
Phillips
A
and Gray
GA
(1961
), Experimental investigation of corners in the yield surface
, ASME J. Basic Eng.
, 83D
, 275
–288
.13.
Save
M
(1961
), On yield conditions in generalized stresses
, Q. Appl. Math.
, 19
(3
), 259
–267
.14.
Thomas TY (1961), Plastic Flow and Fracture in Solids, Academic Press, NY.
15.
Bertsch PK and Findley WF (1962), An experimental study of subsequent yield surfaces: corners, normality, Bauschinger and allied effects, Proc. of 4th US-Natl Congress of Appl Mech, 896.
16.
Mair
WM
and Pugh
HLD
(1964
), Effect of pre-strain on yield surfaces in copper
, J. Mech. Eng. Sci.
, 6
(2
), 150
–163
.17.
Mair
WM
(1967
), An investigation into the existence of corners on the yield surface
, J. Strain Anal. Eng. Des.
, 3
, 188
–195
.18.
Lin
TH
and Ito
M
(1965
), Theoretical plastic distortion of a polycrystalline aggregate under combined and reversed stresses
, J. Mech. Phys. Solids
, 13
, 103
–115
.19.
Miastkowski
J
and Szcepinski
W
(1965
), An experimental study of yield surfaces of prestrained brass
, Int. J. Solids Struct.
, 1
, 189
–194
.20.
Phillips
A
and Sierakowski
RL
(1965
), On the concept of the yield surface
, Acta Mech.
, 1
(1
), 29
–35
.21.
Theocaris
PS
and Hazell
CR
(1965
), Experimental investigation of subsequent yield surfaces using the moire method
, J. Mech. Phys. Solids
, 13
(5
), 281
–294
.22.
Ivlev DD (1966), Ideal Plasticity (in Russian), Science Press, Moscow.
23.
Lin
TH
(1966
), Theoretical plastic stress-strain relationship of a polycrystal and the comparisons with the von Mises and the Tresca plasticity theories
, Int. J. Eng. Sci.
, 4
(5
), 543
–561
.24.
Chait
R
(1972
), Factors influencing the strength differential of high strength steels
, Metall. Trans.
, 3
, 365
–371
.25.
Rauch
GC
and Leslie
WC
(1972
), The extent and nature of the strength-differential effect in steels
, Metall. Trans.
, 3
, 373
–381
.26.
Drucker
DC
(1973
), Plasticity theory, strength differential (SD) phenomenon, and volume expansion in metals and plastics
, Metall. Trans.
, 4
, 667
–673
.27.
Richmond O and Spitzig WA (1980), Pressure dependence and dilatancy of plastic flow, Theoretical and Applied Mechanics, 15th ICTAM.
28.
Casey
J
and Sullivan
TD
(1985
), Pressure dependency, strength-differential effect, and plastic volume expansion in metals
, Int. J. Plast.
, 1
, 39
–61
.29.
Lewandowski
JJ
and Lowhaphandu
P
(1998
), Effects of hydrostatic pressure on mechanical behaviour and deformation processing of materials
, Int. Mater. Rev.
, 43
(4
), 145
–187
.30.
Mogi
K
(1971
), Effect of the triaxial stress system on the failure of dolomite and limestone
, Tectonophysics
, 11
, 111
–127
.31.
Mogi
K
(1972
), Failure and flow of rock
, Tectonophysics
, 13
, 541
–568
.32.
Mogi
K
(1977
), Dilatancy of rocks under general stress states with special reference to earthquake precursors
, J. Phys. Earth
, 25
(Suppl), S203–S217
S203–S217
.33.
Mogi K (1979), Flow and fracture of rocks under general triaxial compresion, Proc of 4th Int Congress on Rock Mechanics (Montreux), A Balkema, Rotterdam, 3, 123–130.
34.
Franklin
JA
and Hoek
E
(1970
), Developments in triaxial test technique
, Rock Mech.
, 2
, 223
–228
.35.
Schickert G (1972), Design of an apparatus for short time testing of concrete under triaxial load, Concrete for Nuclear Reactors, ACI SP34-63, 3, 1355–1376.
36.
Newman
JB
(1974
), Apparatus for testing concrete under multiaxial state of stress
, Mag. Concrete Res.
, 26
(89
), 221
–238
.37.
Reik
G
and Zacas
M
(1978
), Strength and deformation characteristics of jointed media in true triaxial compression
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 15
, 295
–303
.38.
Desai CS et al. (1982), High capacity truly triaxial device, J. Geotech. Testing, March.
39.
Goldscheider M (1982), True triaxial test on dense sand, Constitutive Relations for Soils, G Gudehus, F Darve, and I Vardoulakis (eds), Balkemm, 11–53 and 54–98.
40.
Natau OP, Fro¨hlich BO, and Amuschler TO (1983), Recent development of the large-scale triaxial test, Proc of 5th Congress ISRM (rock mechanics), Melbourne, 1, A65–A74.
41.
Hunsche U (1984), Fracture experiments on cubic rock salt samples, The Mechanical Behavior of Salt, Proc. of 1st Conf, HR Hardy Jr and M Langer (eds) 169–179, Trans Tech Publ, Clausthal.
42.
Michelis
P
(1985
), A true triaxial cell for low and high-pressure experiments
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 22
, 183
–188
.43.
Spetzler
HA
, Sobolev
GA
, Sondergeld
CH
et al. (1986
), Surface deformation, crack formation, and acoustic velocity changes in porophyllite under polyaxial loading
, J. Geophys. Res.
, 86
, 1070
–1080
.44.
Donagle RT, Chaney RC, and Silver ML (eds) (1988) Advance Triaxial Testing of Soil and Rock, (STP-977) ASTM, Philadelphia.
45.
Takahashi M and Koide H (1989), Effect of the intermediate principal stress on strength and deformation behavior of sedimentery rocks at the depth shallower than 2000 m, Rock at Great Depth, V Maury and D Fourmaintraux (eds), Balkema, Rotterdam, 19–26.
46.
Smart
BGD
(1995
), A true triaxial cell for testing cylindrical rock specimen
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 32
(3
), 269
–275
.47.
Crawford
BR
, Smart
BGD
, Main
IG
, and Liakopoulou-Morris
F
(1995
), Strength characteristics and shear acoustic anisotropy of rock core subjected to true triaxial compression
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 32
(3
), 189
–200
.48.
An M and Smart BGD (1998), Determination of upper and lower bounds of poro-elastic constant alpha by compressibility in triaxial stress state, Strength Theory: Applications, Developments, and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 515–520.
49.
Calloch
S
and Marquis
D
(1999
), Triaxial tension-compression tests for multiaxial cycle plasticity
, Int. J. Plast.
, 15
, 521
–549
.50.
Wawersik
WR
, Carson
LW
, Holcomb
DJ
, and Williams
RJ
(1997
), New method for true-triaxial rock testing
, Int. J. Rock Mech. Min. Sci.
, 34
, 330
330
.51.
Haimson
B
and Chang
C
(2000
), A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly granite
, Int. J. Rock Mech. Min. Sci.
, 37
, 285
–296
.52.
Xu
DJ
and Geng
NG
(1984
), Rock rupture and earthquake caused by changing of the intermediate principal stress (in Chinese
), Acta Seismologica Sinica
, 6
(2
), 159
–166
.53.
van Mier
JGM
(1986
), Fracture of concrete under complex stress
, Heron
, 31
(3
), 1
–90
.54.
Xu
DJ
and Geng
NG
(1985
), The variation law of rock strength with increase of intermediate principal stress (in Chinese
), Acta Mechanics Solida Sinica
, 7
(1
), 72
–80
.55.
Li XC and Xu DJ (1990), Experimental verification of the twin shear strength theory–True triaxial test research of strength of the granite in a large power station at Yellow River (in Chinese), Inst of Rock and Soil Mechanics, Chinese Academy of Sciences, Research Report (Rock and Soil), 1990–52.
56.
Geng
NG
(1985
), Earthquakes caused by stress decreasing (in Chinese
), Acta Seismologica Sinica
, 7
(4
), 445
–451
.57.
Xu DJ, Zhang G, and Li TJ (1998), A study of the relationship between intermediate principal stress and rock burst in underground excavation, In: Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds). Science Press, Beijing, New York, 563–568.
58.
Zhang
JZ
and Lin
TJ
(1979
), Stress conditions and the variation of rupture characteristics of a rock as shown by triaxial tests (in Chinese
), Mechanica Sinica
, 11
(2
), 99
–106
.59.
Lin
TJ
and Zhang
JZ
(1981
), The development of engineering strength theories at last decade
, Mech. Pract.
, 3
, 17
–23
.60.
Mazanti BB and Sowers GF (1965), Laboratory testing of rock strength, Proc. of Symp. on Testing Techniques for Rock Mech. Settle, 207–227.
61.
Shen J, Min ZQ, and Gu JC (1998), A new type of material test system-the true tension-compression triaxial facility, Strength Theory: Applications, Developments, and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 551–556.
62.
Gao
YF
and Tao
ZY
(1993
), Examination and analysis of true triaxial compression testing of Strength criteria of rock (English Abstract
), Chin J. Geotech. Eng.
, 15
(4
), 26
–32
.63.
Lu
CS
(1993
), Verification of generalized twin shear strength theory (English abstract
), J. of Mechanical Strength
, 2
, 73
–76
.64.
Lu
CS
(1992
), The application of generalized twin shear stress strength Theory
, Chinese J. of Rock Mechanics and Engineering
, 11
(2
), 182
–189
.65.
Lu
ZT
and Gong
XN
(1997
), Verification of inner and outer envelopes for the yield curve of stable material in deviatoric plane
, Chinese J. of Geotech. Engrg.
, 19
(5
), 1
–5
.66.
Tong
XD
and Gong
XN
(1998
), The properties of the yield curves of the stable materials on the stress plane
, J. Zhejiang Univ (Natural Sci)
, 32
(5
), 643
–647
.67.
ACI Standard 359-74 (1975), ASME Boiler and Pressure Vessel Code, Nuclear Power Plant Components, ACI Standard 359–374.
68.
Jaeger JC and Cook NGW (1979), Fundamentals of Rock Mechanics, third edition, Chapman and Hall, London.
69.
Lade PV (1993), Rock strength criteria-the theories and evidence, Comprehensive rock engineering–Principles, practice, and projects, JA Hudson (ed), Pergamon Press, Oxford UK 1, 255–284.
70.
Hill
JM
and Wu
YH
(1993
), Plastic flows of granular materials of shear index n, (1) yield functions; (2) Plane and axially symmetric problems for n=2,
J. Mech. Phys. Solids
, 40
(1
), 77
–93
, 95–115.71.
Hobbs
DW
(1970
), The behaviour of broken rock under triaxial compression
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 7
, 125
–148
.72.
Franklin
JA
(1971
), Triaxial strength of rock material
, Rock Mech.
, 3
, 86
–98
.73.
Aubertin
M
, Li
L
, Simon
R
, and Khalfi
S
(1999
), Formulation and application of a short-term strength criterion for isotropic rocks
, Can. Geotech. J.
, 36
, 947
–960
.74.
Aubertin
M
, Li
L
, and Simon
R
(2000
), A multiaxial stress criterion for short- and long-term strength of isotropic rock media
, Int. J. Rock Mech. Min. Sci.
, 37
(8
), 1169
–1193
.75.
Griggs
DT
(1936
), Deformation of rocks under high confining pressures
, J. Geol.
, 44
, 541
–577
.76.
Jaeger
JC
(1960
), Rock failure at low confining pressures
, Engineering
, 189
, 283
–284
.77.
Murrell SA (1963), A criterion for brittle fracture of rocks and concrete der triaxial stress and the effect of pore pressure on the criterion under confining pressure, Rock Deformation, Geol. Soc. Am. Mem., 79, 245–274.
78.
Cook
NGW
(1965
), The failure of rock
, Int. J. Rock Mech. Min. Sci.
, 2
, 181
–188
.79.
Broms BB (1966), A note of strength properties of rock, Proc of 1st Congress ISRM (Rock Mechanics), Lisbon, 2, 69–70.
80.
Handin
J
, Heard
HC
, and Magouirk
JN
(1967
), Effect of the intermediate principal stress on the failure of limestone, dolomite and glass at different temperatures and strain rates
, J. Geophys. Res.
, 72
, 611
–640
.81.
Bieniawski
ZT
, Denkhaus
HG
, and Vogler
UW
(1969
), Failure of fractured rock
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 6
, 323
–341
.1.
Brady
BT
(1969
), A statistical theory of brittle fracture for rock materials, Part 1, Brittle failure under homogeneous axisymmetric states of stress, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 6
, 21
–42
; 2.
Part 2,
Brittle failure under homeogenous triaxial states of stress
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 6
, 285
–310
.1.
Michelis
P
and Brown
ET
(1986
), A yield equation for rock
, Can. Geotech. J.
, 23
, 9
–16
.2.
Kawamoto T, Tomita K, and Akimoto M (1970), Characteristics of deformation of rock-like materials under triaxial compression, Proc of 2nd Congress ISRM, Beogradm, 1, 2–2.
3.
Barron
K
(1971
), Brittle fracture initiation in and ultimate failure of rocks, Part 1, Isotropic rock
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 8
, 541
–551
.4.
Barron
K
(1971
), Brittle fracture initiation in and ultimate failure of rocks, Part 2, Anisotropic rock: Theory
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 8
, 553
–563
.5.
Barron
K
(1971
), Brittle fracture initiation in and ultimate failure of rocks, Part 3, Rock: Experiment results
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 8
, 565
–575
.6.
Miller
TW
and Cheatham
JB
(1972
), A new yield condition and hadening rule for rocks
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 9
, 453
–474
.7.
Nascimento U, Falcao CB, Pinelo A, and Marques M (1974), Influence of intermediate stress upon internal friction in block masses, Proc of 3rd Congress ISRM, Denver, 2A, 288–293.
8.
Mogi
K
(1977
), Dilatancy of rocks under general triaxial stress states with special references to earthquake precursors
, J. Phys. Earth
, 25
(Suppl), 5203
–5217
.9.
Gerogiannopoulos
NG
and Brown
EG
(1978
), The critical state concept applied to rock
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 15
, 1
–10
.10.
Brook
N
(1979
), Estimating the traxial strength of rocks
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 16
, 261
–264
.11.
Dragon
A
and Mroz
Z
(1979
), A continuum model for plastic-brittle behavior of rock and concrete
, Int. J. Eng. Sci.
, 17
, 37
37
.12.
Price
AM
and Farmer
IW
(1979
), Application of yield models to rock
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 16
, 157
–159
.13.
Maso
J
and Lerau
J
(1980
), Mechanical behaviour of darny sandstone (Vosges, France) in biaxial compression
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 17
, 109
–115
.14.
Nova
R
(1980
), The failure of transversally isotropic rocks in triaxial compression
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 17
, 325
–332
.15.
Oda
M
, Konishi
J
, and Nemat-Nasser
S
(1980
), Some experimentally based fundamental results on the mechanical behaviour of granular materials
, Geotechnique
, 30
(4
), 479
–495
.16.
Smith
MB
and Cheatham
JB
(1980
), An anisotropic compacting yield condition applied to porous limestone
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 17
, 159
–165
.17.
Lin
TJ
and Zhang
JZ
(1981
), Development of the strength theory for rocks at the last decade (in Chinese
), Mech. Pract.
, 3
, 17
–23
.18.
Blanton
TL
(1981
), Effect of strain rate from 10−2 to 10sec−1 in triaxial compression test on three rocks
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 18
, 47
–62
.19.
Stacey
TR
(1981
), A simple extension strain criterion for fracture of brittle rock
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 18
, 469
–474
.20.
Chiu
HK
, Johnston
JW
, and Donald
IB
(1983
), Appropriate techniques for triaxial testing of saturated soft rock
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 20
, 107
–120
.21.
Amadei B, Janoo V, Robison M, and Kuberan R (1984), Strength of Indiana limestone in true biaxial loading conditions, Rock Mechanics in Productivity and Protection (Proc 24th Symp on Rock Mech), 338–348.
22.
Desai
CS
and Faraque
MO
(1984
), Constitutive model in geological materials
, J. Eng. Mech. Div.
, 110
(9
), 1391
1391
.23.
Lade PV (1984), Failure criterion for frictional materials, Mechanics of Engineering Materials, CS Desai and RH Gallagher (eds), Wiley and Sons, London, 385–402.
24.
Kim
MK
and Lade
PV
(1984
), Modelling rock strength in three dimensions
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 21
(1
), 21
–33
.25.
Tao
ZY
and Mo
HH
(1986
), Study on the strength criterion for rock
, Chin. Sci. Bull.
, 31
(2
), 151
151
.26.
Desai
CS
and Salami
MR
(1987
), A constitutive model and associated testing for soft rock
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 24
, 299
–307
.27.
Desai
CS
and Salami
MR
(1987
), Constitutive model for rocks
, J. Geotech. Eng.
, 113
, 407
–423
.28.
Desai
CS
and Zhang
D
(1987
), Viscoplastic model (for rock) with generalized yield function
, Int. J. Numer. Analyt. Meth. Geomech.
, 11
, 603
–620
.29.
Amadei
B
(1988
), Strength of a regularly joined rock mass under biaxial and axisymmetric loading
, Int. J. Rock. Mech. Min. Sci. Geomech. Abstr.
25
, 3
–13
.30.
Crestescu N (1989), Rock Rheology, Kluwer Acad. Publ, Dordrecht-Boston.
31.
Hunsche U (1989), A failure criterion for natural polycrystalline rock salt, Advance in Constitutive Laws for Eng. Mater., Int Acad Publ, 1043–1046.
32.
Michelis
P
(1989
), True triaxial cyclic behavior of concrete and rock in compression
, Int. J. Plast.
, 3
(2
), 249
–270
.33.
Hunsche
U
and Albrecht
H
(1990
), Results of true triaxial strength tests on rock salt
, Eng. Fract. Mech.
, 35
(4,5), 867
–877
.34.
Wei LL and Hudson JA (1991), An extended H-B criterion as yield surface for rock, Constitutive Law for Engineering Materials, CS Desai, E Kremp, G Frantziskonis, and H Saadatmanesh (eds), ASME, NY.
35.
Yu MH, Liu SH, and An M (1991), The foundational behavior of yield function for rock (in Chinese), The Problems of Rock Mechanics in Hydraulic and Mining Engineering, Science Press, Beijing, 674–679.
36.
Hoek E (1994), Strength of rock masses, Support of Underground Excavations in Hard Rock, E Hoek, PK Kaiser, and WF Bawden (eds), Balkema, Rotterdam, 4–16.
37.
Mroz Z and Maciejewshi J (1994), [TITLE?] Localisation and Bifurcation Theory for Soils and Rocks, R Chambon, J Desrues, and I Vardoulakis (eds) Belkema, Rotterdam, 19–31.
38.
Li
GP
and Tao
ZY
(1995
), A micromechanical damage model for rocks subjected to true triaxial stresses (in Chinese
), Chin J. Geotech. Eng.
, 17
(1
), 24
–31
.39.
Wang R and Kemeny JM (1995), A new empirical failure criterion for rock under polyaxial compressive stresses, Rock Mechanics, JJK Daemen and AA Schultz (eds), AA Balkema, Rotterdam, 453–482.
40.
Yumlu
M
and Ozbay
MU
(1995
), A study of the behavior of brittle rocks under plane strain and triaxial loading conditions
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 32
(7
), 725
–733
.41.
Aubertin
M
and Simon
R
(1997
), A damage initiation criterion for low porosity rocks
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 34
(3-4
), 554
554
.42.
Le XY and Wang YH (1998), A new criterion for rock compression-shear fracture, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 203–208.
43.
Li GP (1998), The damage mechanics of rock subjected to true triaxial compression, Strength Theory, Science Press, New York, Beijing, 181–186.
44.
Nawtocki
PA
and Morz
Z
(1998
), A viscoplastic degradation model for rock-like materials
, Int. J. Rock Mech. Min. Sci.
, 35
(7
), 991
–1000
.45.
Singh
B
, Goel
RK
, Mehrotra
VK
et al. (1998
), Effect of intermediate principal stress on strength of anisotropic rock mass
, Tunn. Undergr. Space Technol.
, 13
(1
), 71
–79
.46.
Tang CA, Fu YF, and Ling P (1998), Numerical simulations of rock failure under multi-axial compression, Strength Theory: Applications, Developments, and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 609–614.
47.
Nawtocki
PA
and Mroz
Z
(1999
), A constitutive model for rock accounting for viscosity and yield stress degradation
, Comp. Geotechn.
, 25
, 247
–280
.48.
Sun
J
and Wang
SJ
(2000
), Rock mechanics and rock engineering in China: Developments and current state-of-the-art
, Int. J. Rock Mech. Min. Sci.
, 37
, 447
–465
.49.
Yu
MH
et al. (2000
), Advances in strength theory of rock in the 20th century (English abstract
), Chin J. Rock Mech. Eng.
, 19
(5
), 545
–550
.50.
Vernik
L
and Zoback
MD
(1992
), Estimation of maximum horizontal principal stress magnitude from stress-induced well bore breakouts in the Cajon Pass scientific research borehole
, J. Geophys. Res.
, 97
, 5109
–5119
.51.
Ewy RT (1992), Wellbore stability predictions using a modified Lade criterion, Proc of Eurock 98: SPE/ISRM Rock Mechanics in Petroleum Engineering, 1, SPE/ISRM Paper No. 47251, 247–254.
52.
Liu
SH
(1994
), Research on the stability of large underground caves under high earth stress in Laxiwa Hydroelectric Power Station, Part A (English abstract
), Hydroelec J. Northwest China
, 4
, 30
–36
.53.
Liu
SH
(1995
), Research on the stability of large underground caves under high earth stress in Laxiwa Hydroelectric Power Station, Part B (English abstract
), Hydrolect J. Northwest China
, 1995
(1
), 42
–50
.54.
Zhou WY et al. (1993), Advanced Rock Mechanics, Water Conservancy and Hydroelectric Power Press, Beijing.
55.
Zhou WY (1993), The development and state of art of rock mechanics in China, Proc of Int Symp on Application of Computer Method in Rock Mechanics and Engineering, Xi’an, China.
56.
Yangtze River Science Institute (1997), Stability of the high rock slopes in the permanent shiplock at Three Gorges on the Yangtze River by using the synthesize analysis method of plastic zones and limit equilibrium, Yangtze River Science Inst, No 97–260.
57.
Wang SJ (1998), Theoretical study and engineering practice of rock mechanics as a branch of modern sciences: Rock mechanics and rock engineering facing to the strategy of sustainable development, Seismology Press, Beijing, 17–21.
58.
Sun J (1999), Rheology of Geomaterials and its Application (in Chinese), China Construction Industry Press, Beijing, 721 pp.
59.
Sun
J
(1999
), Some progress on rock mechanics study in China (English abstract
), W China Explor Eng
, 11
(1
), 1
–5
.60.
Yang
GS
(1999
), On the present state and development of rock mechanics in China
(English abstract), J. Xi; an Mining Ins
, 19
(Suppl), 5
–11
.61.
Li
XJ
, Bei
ZH
, and Zhang
DL
(2000
), Analysis of ultimate inner pressure of ring with different tensile and compressive strength and their application to strength measurements (English abstract
), Rock Soil Mech
, 21
(3
), 264
–266
.62.
Jaeger
JC
(1959
), The frictional properties of joints in rock
, Geofis. Pura Appl.
, 43
, 148
–158
.63.
Brady BT (1966), Limiting equilibrium of fractured and jointed rocks, Proc of 1st Congress ISRM (Rock Mechanics) Lisbon, 1, 531–535.
64.
Goodman RE, Taylor RL, and Brekke TL (1968), A model for the mechanics of jointed rock, J. Soil Mech. Found. Div., 94.
65.
Zienkiewicz OC, Valliappan S, and King P (1968), Stress analysis of rock as a “non-tansion” material, Geotechnique 18, 56–66.
66.
Barton
NR
(1972
), A model study of rock-joint deformation
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 9
, 579
–602
.67.
Barton
NR
(1973
), Review of a new shear strength criterion for rock joints
, Engineering Geology
, 76
, 287
–332
.68.
Barton
NR
(1976
), The shear strength of rock and rock joints
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 13
(10
), 1
–24
.69.
Barton
NR
and Choubey
V
(1977
), The shear strength of rock joints in theory and practice
, Rock Mech.
, 10
(1-2
), 1
–54
.70.
Ghaboussi
J
, Wilson
EL
, and Isenberg
J
(1973
), Finite element analysis for rock joints and interfaces
, J. Soil Mech. Found. Div.
, 99
, 833
–848
.71.
Singh
B
(1973
), Continuum characterization of jointed rock masses, Part 1: The constitutive equations
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 10
, 311
–335
.72.
Singh
B
(1973
), Continuum characterization of jointed rock masses, Part 2: The constitutive equations
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 10
, 337
–349
.73.
Ge XR (1979), The mechanical behaviour and analog analytical method of Joints and weak intercalations in rock mass (in Chinese), Rock-Soil Mech (1,2), 59–72.
74.
Ge XR (1986), Three dimensional infinite elements and joint infinite elements, Chin J. Geotech. Eng., 8(3).
75.
Shiryaev RA, Karpov NM, and Pridorogina IV (1979), Model studies of the strength of jointed rock, Proc. of 4th Congress ISRM, Montreux, 2, 627–632.
76.
Stimpson
B
(1979
), A new approach to simulating rock joints in physical models
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 16
, 215
–216
.77.
Hoek
E
(1983
), Strength of jointed rock masses (1983 Rankine Lecture
), Geotechnique
, 33
(3
), 187
–223
.78.
Heuze
FE
and Barbour
TG
(1982
), New models for rock joints and interfaces
, J. Geotech. Eng.
, 108
(5
), 757
–776
.79.
Desai
CS
and Zaman
MM
et al. (1984
), Thin-layer element for interfaces and joints
, Int. J. Numer. Analyt. Meth. Geomech.
, 8
, 19
–43
.80.
Sheorey
PR
, Biswas
AK
, and Choubey
VD
(1989
), An empirical failure criterion for rock and jointed rock masses
, Eng. Geology
, 26
(2
), 141
–151
.81.
Zhu WS et al. (1992), An equivalent continuous model of joint rock mass and its application (English abstract), Chin. J. Geotech. Eng., 14(2).
82.
Lei
XY
, Swoboda
G
, and Du
QH
(1994
), Theory and application of contact-friction interface element
, J. Geotech. Eng.
, 16
(3
), 23
–32
.83.
Wang GS and Yuan JX (1997), A new method for solving the contact friction problem, Computer Methods and Advances in Geomechanics, JX Yuan (ed), AA Balkema, Rotterdam, 1965–1967.
84.
Zhao
J
(1997
), Joint matching and shear strength, Part A: Joint matching coefficient
, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 34
, 173
–178
.85.
Rossmanith HP (ed), (1998), Mechanics of Joint and Faulted Rock (MJFR-3), AA Balkema, Rotterdam.
86.
Zhao
J
(1998
), A new JRC-JMC shear strength criterion for rock joint
, Chin J. Rock Mech. Eng
, 17
(4
), 349
–357
.87.
Chen
WS
, Feng
XT
, Ge
XR
, and Schweiger
HF
(2000
), A generalized-interface-element method based on static relaxation (in Chinese
), Chin J. Rock Mech. Eng
, 19
(1
), 24
–28
.88.
Bresler
B
and Pister
KS
(1955
), Failure of plain concrete under combined stresses
, Proc. Am. Soc. Civ. Eng.
, 81
, 674
674
.89.
Bresler
B
and Pister
KS
(1958
), Strength of concrete under combined stresses
, ACI Mater. J.
, 55
, 321
–345
.90.
Bellamy
CJ
(1961
), Strength of concrete under combined stress
, ACI Mater. J.
, 58
(10
), 367
–381
.91.
Robison GS (1967), Behavior of concrete in biaxial compression, J. Struct. Engrg. ASCE (1), 71–86.
92.
Nannant
DJ
and Frederick
CO
(1968
), Failure criteria for concrete in compression
, Mag. Concrete Res.
, 20
, 64
64
.93.
Kupfer
H
, Hilsdorf
HK
, and Rusch
H
(1969
), Behavior of concrete under biaxial stresses
, Am. Concr. Inst. J.
, 66
(8
), 656
–666
.94.
Mills
LL
and Zimmerman
RM
(1970
), Compressive Strength of plain concrete under multiaxial loading conditions
, ACI Mater. J.
, 67
(10
), 802
–807
.95.
Rosenthal
I
and Glucklich
J
(1970
), Strength of plain concrete under biaxial stress
, ACI Mater. J.
, 67
(11
), 903
–914
.96.
Buyukozturk
O
, Nilson
AH
, and Slate
FO
(1971
), Stress-strain response and fracture of a concrete model in biaxial loading
, ACI Mater. J.
, 68
(8
), 590
–599
.97.
Liu
TCY
, Nilson
AH
, and Slate
FO
(1972
), Stress-strain response and fracture of concrete in uniaxial and biaxial compression
, ACI Mater. J.
, 69
(5
), 291
–195
.98.
Kupfer
H
and Gerstle
KH
(1973
), Behavior of concrete under biaxial stress
, J. Eng. Mech. Div.
, 99
(4
), 853
–866
.99.
Wu
HC
(1974
), Dual failure criterion for plain concrete
, J. Eng. Mech. Div.
, 100
(6
), 1167
–1181
.100.
Chen
ATC
and Chen
WF
(1975
), Constitutive relations for concrete
, J. Eng. Mech. Div.
, 101
(2
), 465
–481
.101.
Dafalias
YF
and Popov
EP
(1975
), A model of nonlinearly hardening materials for complex loading
, Acta Mech.
, 21
, 173
–192
.102.
Kotsovos
MD
and Newman
JB
(1978
), Generalized stress-strain relation for concrete
, J. Eng. Mech. Div.
, 104
(4
), 845
–856
.103.
Cedolin
L
, Crutzen
YRJ
, and Dei Poli
S
(1977
), Triaxial stress-strain relationship for concrete
, J. Eng. Mech. Div.
, 103
(3
), 423
–439
.104.
Kotsovos
MD
and Newman
JB
(1977
), Behavior of concrete under multiaxial stress
, ACI Mater. J.
, 74
(9
), 443
–446
.105.
Bazant
ZP
and Bhad
PD
(1976
), Endochronic theory of inelasticity and failure of concrete
, J. Eng. Mech. Div.
, 102
(4
), 701
–722
.106.
Nicholas
J
, Carino
J
, and Slate
FO
(1976
), Limiting tensile strain criterion for failure of concrete
, ACI Mater. J.
, 73
(3
), 160
–165
.107.
Tasuji
ME
, Slate
FO
, and Nilson
AH
(1978
), Stress-strain response and fracture of concrete in biaxial loading
, ACI Mater. J.
, 75
(5
), 306
–312
.108.
Ottosen
NS
(1979
), Constitutive model for short-time loading of concrete
, J. Eng. Mech. Div.
, 105
(1
), 127
–141
.109.
Bazant
ZP
and Kim
SS
(1979
), Plastic-fracturing theory for concrete
, J. Eng. Mech. Div.
, 105
(3
), 407
–428
.110.
Gerstle
KH
, Aschl
H
et al. (1980
), Behavior of concrete under multiaxial stress states
, J. Eng. Mech. Div.
, 106
(6
), 1383
–1403
.111.
Michael
D
and Kotsovos
MD
(1979
), Effect of stress path on the behavior of concrete under triaxial stress states
, ACI Mater. J.
, 76
(2
), 213
–223
.112.
Gerstle
KH
, Aschl
H
et al. (1980
), Behavior of concrete under multiaxial stress states
, J. Eng. Mech. Div.
, 106
(6
), 1383
–1403
.113.
Gerstle
KH
(1981
), Simple formulation of biaxial concrete behavior
, ACI Mater. J.
, 78
(1
), 62
–68
.114.
Gerstle
KH
(1981
), Simple formulation of triaxial concrete behavior
, ACI Mater. J.
, 78
(5
), 382
–387
.115.
Hsieh
SS
, Ting
EC
, and Chen
WF
(1982
), A Plasticity-fracture model for concrete
, Int. J. Solids Struct.
, 18
(3
), 181
–197
.116.
Institute of Water Conservancy and Hydroelectric Power Research of China (1982), Translation Collectanea of the Strength and Failure of Concrete (in Chinese), Hydraulic Eng Press, Beijing.
117.
Lade
PV
(1982
), Three parameter failure criterion for concrete
, J. Eng. Mech. Div.
, 108
, 850
–863
.118.
Fardis
MN
, Alibe
B
, and Tassoulas
JL
(1983
), Monotonic and cycle constitutive law for concrete
, J. Eng. Mech.
, 109
(2
), 516
–536
.119.
Yang
BL
, Dafalias
YF
, and Herrmann
LR
(1983
), A bounding surface plasticity model for concrete
, J. Eng. Mech. Div.
, 111
(3
), 359
–380
.120.
Buyukozturk
O
and Tseng
TM
(1984
), Concrete in biaxial cyclic compression
, J. Struct. Engrg., ASCE
, 110
(3
), 461
–476
.121.
Chen RC, Carrasquillo RL, and Fowler DW (1985), Behavior of high strength concrete under uniaxial and biaxial compression, ACI SP-87, 251–273.
122.
Schreyer
HL
and Babcock
SM
(1985
), A third invariant plasticity theory for low-strength concrete
, J. Eng. Mech. Div.
, 111
(4
), 545
–548
.123.
Stankowski
T
and Gerstle
KH
(1985
), Simple formulation under multiaxial concrete behavior
, ACI Mater. J.
, 82
(2
), 213
–221
.124.
Chen
ZD
(1986
), A general failure criterion for short time loading of plain concrete (in Chinese
), J. Hydraul. Eng.
, 31
(2
), 54
–59
.125.
Han
DJ
and Chen
WF
(1987
), Constitutive modeling in analysis of concrete structures
, J. Eng. Mech.
, 113
(4
), 577
–593
.126.
Lin
FB
, Bazant
ZP
, Chern
JC
, and Marchertas
AH
(1987
), Concrete model with normality and sequential identification
, Comput. Struct.
, 26
(6
), 1011
–1025
.127.
Yu MH, Zhao JH et al. (2001), Concrete Strength Theory and its Applications (in Chinese), Higher Education Press, Beijing.
128.
de Boer
R
and Desenkamp
HT
(1989
), Constitutive equations for concrete in failure state
, J. Eng. Mech. Div.
, 115
(8
), 1591
–1608
.129.
Lubliner
J
, Oliver
J
et al. (1989
), A plastic-damage model for concrete
, Int. J. Solids Struct.
, 25
(3
), 299
–326
.130.
Schreyer
HL
(1989
), Smooth limit surfaces for metals: Concrete and geotechnical materials
, J. Eng. Mech. Div.
, 115
(9
), 1960
–1975
.131.
Faruque
MO
and Chang
CJ
(1990
), A constitutive model for pressure sensitive materials with particular reference to plain concrete
, Int. J. Plast.
, 6
(1
), 29
–43
.132.
Bardet
JP
(1990
), Lode dependences for isotropic pressure-sensitive elastoplastic materials
, ASME J. Appl. Mech.
, 57
, 498
–506
.133.
Traina
LA
and Mansor
SA
(1991
), Biaxial strength and deformational behavior of plain and steel fiber concrete
, ACI Mater. J.
, 88
(4
), 354
–362
.134.
Chern
JC
, Yang
HJ
, and Chen
HW
(1992
), Behavior of steel fiber reinforced concrete in multiaxial loading
, Amr. Concr. Ins. Material. J.
, 89
(1
), 32
–40
.135.
Bazant
ZP
and Ozbolt
J
(1992
), Compression failure of quasibrittle material: Nonlocal microplane model
, J. Eng. Mech. Div.
, 118
(3
), 540
–556
.136.
Ozbolt
J
and Bazant
ZP
(1992
), Microplane model for cyclic triaxial behavior of concrete
, J. Eng. Mech. Div.
, 118
(7
), 1365
–1386
.137.
Abu-Lebdeh
TM
and Voyiadjis
GZ
(1993
), Plasticity-damage model for concrete under cyclic multiaxial loading
, J. Eng. Mech.
, 119
(7
), 1465
–1484
.138.
Labbane
M
, Saha
NK
, and Ting
EC
(1993
), Yield criterion and loading function for concrete plasticity
, Int. J. Solids Struct.
, 30
(9
), 1269
–1288
.139.
Song
YB
, Zhao
GF
, Peng
F
et al. (1993
), Strength characteristics of light-concrete under tri-axial compression (in Chinese
), J. Hydraul. Eng.
, 38
(6
), 10
–16
.140.
Voyiadjis
GZ
and Abu-Lebdeh
TM
(1993
), Damage model for concrete using bounding surface concept
, J. Eng. Mech.
, 119
(9
), 1865
–1885
.141.
Song
YP
, Zhao
GF
, and Peng
F
(1994
), Strength behavior and failure criterion of steel fibre concrete under triaxial stresses (in Chinese
), China Civil Eng. J
, 27
(3
), 14
–23
.142.
Bresler B and Pister KS (1995), Failure of plain concrete under combined stresses, ASCE Trans, Proc.-Separate No. 674, April.
143.
Feenstra
PH
and de Borst
R
(1996
), A composite plasticity model for concrete
, Int. J. Solids Struct.
, 33
(5
), 707
–730
.144.
Qian
ZZ
and Qian
C
(1996
), Strength criterion of concrete under multiaxial loading condition
, China Civil Eng. J
, 29
(2
), 46
–54
.145.
Balan
TA
, Filippou
FC
, and Popov
EP
(1997
), Constitutive model for 3D cycle analysis of concrete structures
, J. Eng. Mech. Div.
, 123
(2
), 143
–153
.146.
Li
JK
(1997
), Experimental research on behavior of high strength concrete under combined compressive and shearing loading (in Chinese
), China Civil Engrg. J.
, 30
(3
), 74
–80
.147.
Fan SC, Wang F, and Yu MH (1998), Generalisation of unified strength criterion for concrete, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SO Fan (eds), Science Press, Beijing, New York, 386–392.
148.
He XG, Kwan AKH, and Chan HC (1998), Limiting tensile strain failure criterion for concrete, Strength Theory, Science Press, 397–402.
149.
Li QB and Ansari F (1998), Failure criterion for high strength concrete subjected to triaxial compression, Strength Theory, Science Press, 415–420.
150.
Li QB and Ansari F (1998), Effect of specimen size in testing of high strength concrete subjected to triaxial compression, Strength Theory, Science Press, 541–546.
151.
Makitani E (1998), Research on shear resistance of reinforced concrete column with high strength reinforcement and concrete, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 421–426.
152.
Perry SH (1998), Blast and hard impact damaged concrete, causes and consequences, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 465–470.
153.
Tan TH and Cheong HK (1998), An apparatus for testing concrete under active and passive confining stress, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 557–562.
154.
Xie S, Makitani E, Mizukami, A, and Onodera T (1998), Research on the shear transfer mechanism of the joint connection in precast reinforced concrete structure, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 433–438.
155.
Zeng WB and Wei XY (1998), Computer simulation of failure criteria for concrete, Strength Theory, Science Press, Beijing, New York, 639–642.
156.
Zhao
JH
et al. (1999
), A new method to calculate the limit load of concrete rectangular plate (in Chinese
), Engineering Mechanics
, 16
(2
), 121
–126
.157.
Li
QB
and Ansari
F
(1999
), Mechanics of damage and constitutive. relationships for high-strength concrete in triaxial compression
, J. Eng. Mech.
, 25
(1
), 1
–10
.158.
Li JC (2001), Investigation of High Velocity Long Rod Penetrating Semi-infinite Concrete Target, PhD Thesis, (in Chinese), Xi’an Jiaotong Univ, Xi’an, China.
159.
Xu JS (1984), Strength Theory and its Application (in Chinese), Hydraulic Press, Beijing.
160.
Nilsson AH (1968), Nonlinear analysis of reinforced concrete by the finite element method, ACI, 65(9).
161.
Valliappan S and Doolan TF (1972), Nonlinear stress analysis of reinforced concrete, J. Struct. Div. ASCE, 98(4).
162.
Zienkiewicz
OC
, Owen
DRH
, Phyillips
DV
, and Hyak
GC
(1970
), Finite element method in analysis of reactor vessels
, Nuclear Engrg & Design
, 20
, 507
-541
.163.
Argyris
JH
, Faust
G
, Szimmat
J
, Warnke
EP
, and Willam
KJ
(1974
), Recent developments in the finite element analysis of prestressed concrete reactor vessels
, Nucl. Eng. Des.
, 28
, 42
–75
.164.
Buyukozturk
O
(1977
), Nonlinear analysis of reinforced concrete structure
, Comput. Struct.
, 7
(1
), 149
–156
.165.
Bathe
KJ
and Ramaswang
S
(1979
), On three-dimensional nonlinear analysis of concrete structures
, Nucl. Eng. Des.
, 52
(3
), 385
–409
.166.
Bangash MY (1989), Concrete and Concrete Structures: Numerical Modelling and Applications, Elsevier, London.
167.
Frangopol
DM
, Fee
YH
, and William
KJ
(1996
), Nonlinear finite element reliability analysis of concrete
, J. Eng. Mech.
, 122
(12
), 1174
–1182
.168.
Guo
DF
, Liang
XM
, and Wang
F
(1997
), Nonlinear finite element analysis of deep beam of reinforced concrete (by using of the unified strength theory, (in Chinese
), J. of Xxian Jiaotong Univ.
31
(6
), 83
–88
.169.
Mchrabi
AB
and Shing
PB
(1997
), Finite element modeling of masonry-infilled reinforced concrete frames
, J. Struct. Engrg.
123
(5
), 604
–613
.170.
Wang F (1998), Nonlinear finite element analysis of RC plate and shell using unified strength theory, PhD Thesis, Nanyang Technological Univ., Singapore.
171.
Nakano M and Shi ZH (1998), Implementation of the energy criterion in numerical modeling of reinforced concrete behaviors after cracking, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 427–432.
172.
Habib MP (1953), Influence of the variation of the intermediate principal stress on the shearing strength of soils, Proc of 3rd Int Conf Sial Mech Foundation Eng, 1, 131–136.
173.
Drucker
DC
, Gibson
RE
, and Henkel
DJ
(1957
), Soil mechanics and work hardening theories of plasticity
, Trans. Am. Soc. Civ. Eng.
, 122
, Paper No. 2864, 338
–346
.174.
Haythornwaite RM (1960), Stress and strain in soils, Plasticity, EH Lee and PS Symonds (eds), Pergamon Press, Oxford, 185–193.
175.
Haythornwaite RM (1960), Mechanics of the triaxial test for soils, J. Soil Mech. Found. Div., 86(5).
176.
Roscoe
KH
, Schofield
AN
, and Thurairajah
A
(1963
), Yielding of clays in states wetter than critical
, Geotechnique
, 13
(3
), 211
–240
.177.
Fang KZ (1964), Mechanical strength theory for soils, Res. Report of Xi an Jiaotonl University, Xi’an.
178.
Broms BB and Casbarian AO (1965), Proc of 6th Int Conf on Soil Mechanics and Foundation Engineering, 1, 179–183.
179.
Bishop
AW
(1966
), The Strength of soils as engineering materials (Sixth Rankine Lecture
), Geotechnique
, 16
(2
), 91
–130
.180.
Poorooshasb
HB
, Holubec
I
, and Sherbourne
AN
(1966
), Yielding and flow of sand in triaxial compression: Part I
, Can. Geotech. J.
, 3
(4
), 179
–190
.181.
Poorooshasb
HB
, Holubec
I
, and Sherbourne
AN
(1967
), Yielding and flow of sand in triaxial compression: Parts II and III
, Can. Geotech. J.
, 4
(4
), 376
–397
.182.
Roscoe KH and Burland JB (1968), On the generalized stress-strain behaviour of wet clay, Engineering Plasticity, Cambridge Univ 1, 535.
183.
Vesic
AS
and Clough
GW
(1968
), Behaviour of granular materials under high stresses
, J. Soil Mech. Found. Div.
, 94
(3
), 661
–688
.184.
Green
RJ
(1972
), A plastic theory for porpous solids
, Int. J. Mech. Sci.
, 14
(4
), 215
–224
.185.
Green GE (1972), Strength and deformation of sand measured in an independent stress control cell, Stress-Strain Behaviour of Soils, RHG Parry (ed), Foulis Co Ltd, 285–323.
186.
Sutherland HB and Mesdary MS (1969), The influence of the intermediate principal stress on the strength of sand, Proc of 7th Int Conf on Soil Mechanics and Foundation Engineering, 1, 391–399.
187.
Lade
PV
and Duncan
JM
(1973
), Cubical triaxial tests on cohesionless soil
, J. Soil Mech. Found. Div.
, 99
(10
), 793
–812
.188.
Tasuoka
F
and Ishihara
K
(1974
), Yielding of sand in triaxial compression
, Soils Found.
, 14
(2
), 63
–76
.189.
Chen WF (1975), Limit Analysis and Soil Plasticity, Elsevier, Amsterdam.
190.
Wong
PK
and Mitchell
RJ
(1975
), Yielding and plastic flow of sensitive cemented clay
, Geotechnique
, 25
(4
), 763
–782
.191.
Mroz
Z
, Norris
VA
, and Zienkiewicz
OC
(1978
), An anisitropic hardening model for soil and its application to cyclic loading
, Int. J. Numer. Analyt. Meth. Geomech.
, 2
(3
), 203
–221
.192.
Vermeer
PA
(1978
), A double hardening model for sand
, Geotechnique
, 28
(4
), 413
–433
.193.
Tavenas
F
et al. (1979
), The use of strain energy as a yield and creep criterion for lightly overconsolidated clays
, Geotechnique
, 29
(3
), 285
–303
.194.
Tang
L
(1981
), The failure criterion of sand (in Chinese
), Chinese J. of Geotech. Eng.
3
(2
), 1
–7
.195.
Ghaboussi J, Kim KJ, and Momen H (1982), Modeling and predication of behavior of sand under arbitrary stress paths, Constitutive Relations for Soils, G Gudehus, F Darve, and I Vardoulakis (eds), Balkeman, 215–356.
196.
Goldscheider M (1982), True triaxial test on dense sand, Constitutive Relations for Soils, G Gudehus, F Darve, and I Vardoulakis (ed), Balkemm, 11–53 and 54–98.
197.
Butterfield R and Harkness RM (1972), The kinematics of Mohr-Coulomb materials, Stress Strain Behaviour of Soils, RHG Parry (ed), Foulis Co Ltd, 220–233.
198.
Zienkiewicz OC and Humpheson C (1977), Viscoplasticity: A generalized model for description of soil behavior, Numerical Methods in Geotechnical Engineering, CS Desa and JT Christian (eds).
199.
Mroz
Z
, Norris
VA
, and Zienkiewicz
OC
(1979
), Application of an anisotropic hardening model in the analysis of elastoplastic deformation of soils
, Geotechnique
, 29
(1
), 1
–34
.200.
Matsuoka H and Nakai T (1977), Proc of 9th Int Conf on Soil Mech and Found Eng, 158–162.
201.
Dafalias YF and Herrmann R (1980), A boundary surface soil plasticity model, Int Symp on Soil under Cycle and Transient Loading, Swansea.
202.
Desai
CS
(1980
), A general basis for yield, failure and potential functions in plasticity
, Int. J. Numer. Analyt. Meth. Geomech.
, 4
(4
), 361
–375
.203.
Huang
WQ
, Pu
JL
, and Chen
YJ
(1981
), Hardening rule and yield function of soils (in Chinese
), Chinese J. of Geotech. Eng
3
(3
), 19
–26
.204.
Dafalias YF and Herrmann LR (1982), Bounding surface formulation of soil plasticity, Soil Mechanics-Trancient and Cyclic Loads, GN Pande and OC Zienkiewicz (ed), John Wiley & Sons, New York, 253–282.
205.
Houlsby GT, Wroth CP, and Wood DM (1982), Predictions of the results of labratory tests, Constitutive Relations for Soils, G Gudehus, F Darve, and I Vardoulakis (eds), A A Balkem, 11–53 and 99–214.
206.
Zienkiewicz
OC
(1982
), Generalized plasticity and some models for geomechanics (in Chinese
), Appl. Math. Mech.
, 3
(3
), 267
–280
.207.
Zienkiewicz
OC
(1982
), Basic formulation of static and dynamic behaviours of soil and other porous media (in Chinese
), Appl. Math. Mech.
, 3
(4
), 417
–428
.208.
Hardin
BO
(1983
), Plane strain constitutive equations for soils
, J. Geotech. Eng.
, 109
(3
), 388
–407
.209.
Cailletaud
G
, Kaczmarck
H
, and Policella
H
(1984
), Some elements on multi axial behavior of 316 stainless steel room temperature
, Mech. Mater.
, 3
, 333
333
.210.
Chen WF (1984), Constitutive modeling in soil mechanics, Mechanics of Engineering Materials, CS Desai and RH Gallagher (ed), John Wiley & Sons Ltd.
211.
Gudehus G, Darve F, and Vardoulakis I (eds) (1984), Constitutive Relations for Soils, Balkema, Rotterdam.
212.
Vermeer PA (1984), [TITLE?] Constitutive Relations for Soils, G Gudehus, F Darve and I Vardoulakis (ed), Balkema, Rotterdam, 184.
213.
Wood DM (1984), Choice of models for geotechnical predictions, CS Desai and RH Gallagher Mechanics of Engineering Materials, (eds) John Wiley & Sons. Chichester, 633–654.
214.
Fang
KZ
(1986
), Failure criterion for soil: influence of intermediate principal stress (in Chinese
), J. of Hohai Univ.
14
(2
), 70
–81
.215.
Houlsby
GT
(1986
), A general failure criterion for frictional and cohesive materials
, Soils Found.
, 26
(2
), 97
–101
.216.
Pu
JL
and Li
GX
(1986
), State of the art (2): Constitutive laws of soil and their evaluation and applications
, Chinese J. of Geotech Soc
, 71
(5
), 343
–348
.217.
Zhang
XY
and Janbu
(1986
), Review of the system of soil mechanics (in Chinese
), Adv Mech
16
(1
), 40
–53
.218.
Miura F and Toki K (1987), Estimation of natural frequency and damping factor for dynamic soil structure interaction systems, Soil-Structure Interaction, AS Cakmak (ed), Elsevier, Amsterdam.
219.
Runesson
K
(1987
), Implicit integration of elasto-plastic relations with reference to soils
, Int. J. Numer. Analyt. Meth. Geomech.
, 11
, 315
–321
.220.
Saleeb
AF
and Chen
WF
(1987
), Survey of constitutive relations for soil (in Chinese
), Ad Mech
17
(2
), 261
–268
.221.
Shen
ZJ
(1989
), Development of constitutive modeling of geological materials (in Chinese
), Rock Soil Mech
10
(2
), 3
–13
.222.
Zheng YR and Gong XN (1989), Foundamentals of Plasticity in Geomechanics (in Chinese), China Construction Industry Press, Beijing.
223.
de Boer
R
(1988
), On plastic deformation of soils
, Int. J. Plast.
, 4
, 371
–391
.224.
Matsuoka
H
, Hoshikawa
T
, and Ueno
K
(1990
), A general failure criterion and stress-strain relation for granular materials to metals
, Soils Found.
, 30
(2
), 119
–127
.225.
Gutierrez M (1991), Modelling the combined effects of the intermediate principal stress and initial anisotropy on the strength of sand, Constitutive Law for Engineering Materials, CS Desai, E Krempl, G Frantzis-konis, and H Saadatmanesh (eds) ASME Press, New York, 129–132.
226.
Xing
RC
, Liu
ZD
, and Zheng
YR
(1992
), A failure criterion of loess (in Chinese
), J. Hydraul. Eng.
, 37
(1
), 12
–19
.227.
Yu
MH
and Meng
XM
(1992
), Twin shear elasto-plastic model and its application in geotechnical engineering
, Chinese J. of Geotech. Eng
14
(3
), 71
–75
(English Abstract).228.
Shen
ZJ
(1993
), Comparison of several yield criteria (in Chinese
), Rock Soil Mech
14
(1
), 41
–50
.229.
Borja
RI
et al. (1994
), Multiaxial cyclic plasticity in clay
, J. Geotech. Eng.
, 120
(6
), 1051
–1070
.230.
Brinkgreve RBJ, Vermeer PA, and Vos E (1994), Constitutive aspects of an embankment widening project, Advances in Understanding and Modeling the Technical Behaviour of Peat, den Haan et al. (eds), Balkema, Rotterdam, 143–158.
231.
Lade PV (1995), Three-dimensional strength of porous materials, Beitrage zur Mechanik, 259–269.
232.
Shahrour I and Kasdi A (1995), in: Numerical Models in Geomechanics, GN Pande and S Pietruszczak (eds), Balkema, Rotterdam, 133–138.
233.
Shen
ZJ
(1995
), A double hardening model for clays (in Chinese
), Rock Soil Mech
16
(1
), 1
–8
.234.
Jiang
MJ
and Shen
ZJ
(1996
), Unified solution to expansion of cylindrical cavity for geomaterials with strain-softening behaviour (using the unified strength theory, in Chinese
), Rock Soil Mech
17
(1
), 1
–8
.235.
Jiang
MJ
and Shen
ZJ
(1996
), Expansion of cylindrical cavity with elastic-brittle-plastic softening and shear dilatation behaviour (using the unified strength theory, in Chinese
), J. Hohai Univ
24
(4
), 65
–72
.236.
Michalowski
RL
and Zhao
A
(1996
), Failure of fiber-Reinforced granular soils
, J. Geotech. Eng.
, 122
(3
), 226
–234
.237.
Wang
HJ
, Ma
QG
, Zhou
JX
et al. (1996
), A study of dynamic characteristics of soil in complex stress state (in Chinese
), J. Hydraul. Eng.
, 41
(4
), 57
–64
.238.
Xu
YF
and Shi
CL
(1997
), Strength characteristics of expansive soils (in Chinese
), J. of Yangtze River Sci Res Ins
4
(1
), 38
–41
.239.
Hashiguchi K (1998), Elastoplastic constitutive model with time-dependency and its application to soils, Strength Theory, Science Press, Beijing, New York, 239–244.
240.
Liao HJ and Yu MH (1998), Application of twin shear strength theory in soil liquefaction, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 245–252.
241.
Sawicki
A
(1998
), Developments in the mechanics of reinforced soil: Empirrical background and analytical approaches
, Appl. Mech. Rev.
, 51
(11
), 651
–668
.242.
Yin JH (1998), Yield and failure criteria and generalized three-moduli nonlinear constitutive model for soils, Strength Theory, Science Press, Beijing, New York, 291–300.
243.
Matsuoka H, Sun DA, and Yao YP (1998), 3-D failure and yield criteria for geometerials based on spatially mobilized plane(smp), Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds) Science Press, Beijing, New York, 260–266.
244.
Mattsson
H
, Axelsson
K
, and Klisinski
M
(1999
), On a constitutive driver as a useful tool in soil plasticity
, Adv. Eng. Software
, 30
, 511
–528
.245.
Shen ZJ (2000), Theoretical Soil Mechanics, Water Conservancy and Hydroelectric Power Press, Beijing, 330 pages.
246.
Frost
JD
and Han
J
(1999
), Behavior of interfaces between fiberreinforced polymers and sands
, J. Geotech. Geoenviron. Eng.
125
(8
), 633
–640
.247.
Schreyer
HL
and Bean
JE
(1985
), A third invariant visco plasticity theory for rate-dependent soils
, J. Geotech. Eng.
, 112
(2
), 181
–192
.248.
Schreyer HL and Wang ML (1990), In: Micromechanics of Failure of Quasi-Brittle Materials, SP Shah, SE Swartz, and ML Wang (ed), Elsevier, London, 95–104.
249.
Ehlers
W
(1995
), A single-surface yield function for geomaterials
, Arch. Appl. Mech.
, 65
, 246
–259
.250.
Zhang
JM
and Zhao
SJ
(1988
), Dynamic strength criterion on sands under the 3-D condition (in Chinese
), J. Hydraul. Eng.
, 33
(3
), 54
–59
.251.
Roscoe
KH
, Schofield
AN
, and Wroth
CP
(1958
), On the yielding of soils
, Geotechnique
, 8
(1
), 22
–52
.252.
Roscoe KH and Poorooshash HBA (1963), A theoretical and experimental study of strain in triaxial compression tests on normally consolidated clay, Geotechnique, 13(1).
253.
Schofield AN and Wroth CP (1968), Critical State Soil Mechanics, McGrw-Hill, London.
254.
Dimaggio
FL
and Sandler
IS
(1971
), Material model for granular soils
, J. Eng. Mech. Div.
, 97
(3
), 935
–950
.255.
Sandler
IS
, DiMaggio
FL
, and Baladi
GY
(1976
), Generalized cap model for geological materials
, J. Geotech. Eng.
, 102
(7
), 683
–699
.256.
Atkingson JH and Bransby PL (1978), The Mechanics of Soils: An Introduction to Critical State Soil Mechanics, McGraw-Hill, Maidenhead.
257.
Atkingson JH (1981), Foundations and Slops, An Introduction to Application of Critical State Soil Mechanics, McGraw-Hill, Maidenhead.
258.
Mroz
Z
, Norris
VA
, and Zienkiewicz
OC
(1981
), An anisotropic critical state model for soils subject to cyclic loading
, Geotechnique
, 31
(4
), 451
–469
.259.
Resende
L
and Martin
JB
(1985
), Formulation of Drucker-Prager cap model
, J. Eng. Mech. Div.
, 111
(7
), 855
–881
.260.
Faruque
MO
and Chang
CJ
(1986
), A new cap model for failure and yielding of pressure-sensitive materials
, J. Eng. Mech. Div.
, 112
(11
), 1041
–1053
.261.
Ortigao JAR (1995), Soil Mechanics in the light of critical State Theories: An Introduction, Balkema Rotterdam.
262.
Mroz
Z
(1967
), On the description of anisotropic work-hardening
, J. Mech. Phys. Solids
, 15
, 163
–175
.263.
Iwan
WD
(1967
), On a class of models for the yielding behavior of continuous and composite systems
, ASME J. Appl. Mech.
, 34
(3
), 612
–617
.264.
Krieg
RD
(1975
), A practical two-surface plasticity theory
, ASME J. Appl. Mech.
, 42
, 641
641
.265.
Prevost
JH
(1978
), Plasticity theory for soil stress behavior
, J. Eng. Mech. Div.
, 104
(5
), 1177
–1194
.266.
Prevost
JH
(1982
), Two surfaces vs multi-surface plasticity theory
, Int. J. Numer. Analyt. Meth. Geomech.
, 6
(3
), 323
–338
.267.
Shen
ZJ
(1984
), A stress-strain model for soils with three yield surfaces (in Chinese
), Acta Mech Solida Sinica
, 6
(2
), 163
–174
.268.
McDowell
DL
(1985
), A two surface model for transient nonproportional cyclic plasticity: Part 1 and 2
, ASME J. Appl. Mech.
, 52
, 298
298
.269.
Hirain
H
(1987
), Soils Found.
, 27
, 1
1
.270.
Simo
JC
, Kennedy
JG
, and Govindjee
S
(1988
), Non-smooth multisurface plasticity and viscoplasticity, Loading and unloading conditions and numerical algorithms
, Int. J. Numer. Methods Eng.
, 26
, 2161
–2186
.271.
Pan
YW
(1991
), Generalized nonassociative multisurface approach for granular materials
, J. Geotech. Eng.
, 117
(1
), 51
–65
.272.
Zheng YR (1993), Plasticity of multi-yielding surfaces and constitutive model for soil (in Chinese), Plasticity and Mesomechanics, Peking Univ Press, Beijing, 75–84.
273.
Lourenco
PB
and Rots
JG
(1997
), Multisurface interface model for analysis of masonary structures
, J. Eng. Mech.
, 123
(7
), 660
–668
.274.
Sawicki
A
(1981
), Yield conditions for layered compositees
, Int. J. Solids Struct.
, 17
(10
), 969
–979
.275.
Grassi
RC
and Cornet
J
(1949
), Fracture of gray cast iron tubes under biaxial stress
, ASME J. Appl. Mech.
, 71
, 178
–182
.276.
Coffin
LF
(1950
), The flow and fracture of a brittle material
, ASME J. Appl. Mech.
, 72
, 233
–248
.277.
Fischer
FC
(1952
), A criterion for the failure of cast iron
, ASTM Bull.
, 181
, 74
–75
.278.
Cornet
J
and Grassi
RC
(1955
), Fracture of inokulated iron under biaxial stress
, ASME J. Appl. Mech.
, 77
(2
), 172
–174
.279.
Cornet
I
and Grassi
RC
(1961
), ASME J. Basic Eng.
, 83
(1
), 39
–44
.280.
Mair
WM
(1968
), Fracture criterion for cast iron under biaxial stresses
, J. Energy Div. (Am. Soc. Civ. Eng.)
, 3
, 254
–263
.281.
Pisarenko GS and Lebedev AA (1969), Deformation and Fraeture of Mateerials under Combined Stress (in Russian), Izd. Naukoea Dumka, Kiev.
282.
Yang
BJ
and Dantzig
JA
(1992
), Stress yield surface and modeling of 3-D thermoelasto-plastic stress development for gray iron castings
, J. Xi’an Jiaotong Univ
, 26
(4
), 37
–46
.283.
Hjelm
HE
(1994
), Yield surface for grey cast iron under biaxial stress
, ASME J. Eng. Mater. Technol.
, 116
, 148
–154
.284.
Hu
LW
and Bratt
JF
(1958
), Effect of tensile plastic deformation on yield condition
, ASME J. Appl. Mech.
, 22
(1
), 411
411
.285.
Hu
LW
(1959
), Development of a triaxial stress testing machine and triaxial stress experiments
, Emiss. Contin. Combust. Syst., Proc. Symp.
, 16
, 27
–37
.286.
Jenike
AW
and Shield
RT
(1959
), On the plastic flow of Coulomb solids beyind original failure
, ASME J. Appl. Mech.
, 26
, 599
–602
.287.
Palmer
AC
, Maier
G
, and Drucker
DC
(1967
), Normality relations and convexity of yield surfaces for unstable materials or structural elements
, ASME J. Appl. Mech.
, E34
(2
), 464
–470
.288.
Zyczkowski
M
(1967
), Combined loadings in the theory of plasticity
, Int. J. Non-Linear Mech.
, 2
, 173
–205
.289.
Powell
WR
(1968
), A note on yield curve in cyclic work softening
, ASME J. Appl. Mech.
, 35
(4
), 822
–824
.290.
Shiratori
E
and Ikegami
K
(1968
), Experimental study of the subsequent yield surface by using cross-shaped specimens
, J. Mech. Phys. Solids
, 16
, 1482
–1490
.291.
Sierakowski
RL
and Phillips
A
(1968
), The effect of repeated loading on the yield surface
, Acta Mech.
, 6
(2–3
), 217
–231
.292.
Sub NP (1969), A yield criterion for plastic frictional work-hardening granular materials, Int. J. Powder Metall., 5(1).
293.
Rogan
H
and Shelton
A
(1969
), Yield and subsequent flow behaviour of some annealed steels under combined stress
, J. Strain Anal. Eng. Des.
, 4
(2
), 127
–137
.294.
Rogan
H
and Shelton
A
(1969
), Effect of pre-stress on the yield and flow of En 25 steel
, J. Strain Anal. Eng. Des.
, 4
(2
), 138
–161
.295.
Mansfield
EH
(1971
), Biaxial yield criteria
, J. R. Aeronaut. Soc.
, 75
(732
), 849
–850
.296.
Dubey
RN
and Hillier
MJ
(1972
), Yield criteria and the Bauschinger effect for a plastic solids
, ASME J. Basic Eng.
, D94
(1
), 228
–230
.297.
Phillips
A
, Liu
CS
, and Justusson
JW
(1972
), An experimental investigation of yield surfaces at elevated temperatures
, Acta Mech.
, 14
(2–3
), 119
–146
.298.
Phillips
A
and Tang
JL
(1972
), The effect of loading path on the yield surface at elevated temperatures
, Int. J. Solids Struct.
, 8
(4
), 463
463
.299.
Hartzmann
M
(1973
), Stress-strain relation for materials with different tension, compression derungen
, AIAA J.
, 11
(3
), 378
–379
.300.
Inoue T, Tanaka K, and Izshizaki T (1973), Yield surfaces of metals at elevated temperatures, Japan Congress of Material Research, 126–131.
301.
McLaughlin
PV
(1973
), Properties of work-hardening materials with a limit surface
, ASME J. Appl. Mech.
, 40
, 803
803
.302.
Michno
MJ
and Findley
WN
(1973
), Experiments to determine small offset yield surfaces of 304L stainless steel under combined tension and torsion
, Acta Mech.
, 18
(3–4
), 163
–179
.303.
Michno
MJ
and Findley
WN
(1974
), Subsequent yield surface for annealed mild steel under dead-weigh loading:aging, normality, coners, Bauschinger and cross effects
, ASME J. Eng. Mater. Technol.
, H96
(1
), 56
–64
.304.
Michno
MJ
and Findley
WN
(1975
), Subsequent yield surfaces for annealed mild steel under servo-controlled strain and load histories: aging, normality, convexity, corners, Bauschinger and cross effects
, ASME J. Eng. Mater. Technol.
, 97
(1
), 25
–32
.305.
Ohashi
Y
and Tokuda
M
(1973
), Precise measurement of plastic behaviour of mild steel tubular specimens subjected to combined torsion and axial force
, J. Mech. Phys. Solids
, 21
(4
), 241
–261
.306.
Phillips
A
and Kasper
R
(1973
), On the foundations of thermoplasticity, an expermental investigation
, ASME J. Appl. Mech.
, E40
(4
), 891
–896
.307.
Shrivastava
HP
, Mroz
Z
, and Dubey
RN
(1973
), Yield criteion and hardening rule for a plastic solids
, Z. Angew. Math. Mech.
, 53
(10
), 625
–633
.308.
Shrivastava
HP
, Mroz
Z
, and Dybey
RN
(1973
), Yield condition and second-order effects in plane stress
, Acta Mech.
, 17
, 137
–143
.309.
Botdorf
SB
and Crose
JG
(1974
), A statistical theory for the fracture of brittle structures subjected to nonuniform polyaxial stress
, ASME J. Appl. Mech.
, 41
, 459
–464
.310.
Ohashi
Y
, Tokuda
M
, and Mizuno
S
(1974
), A precise stress-strain relation of mild steel in the proportional deformation under combinebd loading
, Bull. JSME
, 17
(111
), 1135
–1142
.311.
Phillips
A
, Tang
JL
, and Ricciuti
M
(1974
), Some new observations of yield surfaces
, Acta Mech.
, 20
(1–2
), 23
–29
.312.
Shrivastava
HP
and Dubey
RN
(1974
), Yield condition and hardening rule for density varying materials
, Z. Angew. Math. Mech.
, 54
(9
), 594
–596
.313.
Sewell
MJ
(1974
), A plastic flow rule at a yield vertex
, J. Mech. Phys. Solids
, 22
(6
), 469
–490
.314.
Inoue
T
and Tanaka
K
(1975
), Subsequent yield conditions of mental under cyclic loading at elevate temperatures
, Ing-Archiv
, 44
(2
), 53
–62
.315.
Naghdi
PM
and Trapp
JA
(1975
), The significance of formulating plasticity theory with reference to loading surfaces in strain space
, Int. J. Eng. Sci.
, 13
, 785
785
.316.
Ohashi
Y
, Tokuda
M
, and Yamashita
H
(1975
), Plastic deformation of mild steel under combined load of axial force and torsion with strain trajectory of constant curvature
, Bull. JSME
, 18
(120
), 579
–586
.317.
Hecker SS (1976), Experimental studies of yield phenomena in biaxially loaded metals, ASME, AD-20, 1.
318.
Moon
H
(1976
), An experimental study of the outer yield surface for annealed polycrystalline alumimium
, Acta Mech.
, 24
, 191
–208
.319.
Deneshi
GH
et al. (1976
), Int. J. Mech. Sci.
, 18
, 195
195
.320.
Phillips
A
and Moon
H
(1977
), An experimental investigation concerning yield surfaces and loading surfaces
, Acta Mech.
, 27
, 91
–102
.321.
Phillips
A
and Lee
CW
(1979
), Yield surfaces and loading surfaces. Experiments and recommendations
, Int. J. Solids Struct.
, 15
, 715
–729
.322.
Yu
MH
(1979
), Investigations on macroscopic strength theory of isotropic materials (in Chinese
), J. Xian Jiaotong Univ
, 13
(3
), 113
–119
.323.
Drucker
DC
and Palgen
L
(1981
), On stress-strain relations suitable for cycle and other loading
, ASME J. Appl. Mech.
, 48
, 479
–485
.324.
Yu
MH
and He
LN
(1983
), Twin shear stress criterion of plastic deformation in metals
, Chinese Science Bull (English edition)
, 28
(8
), 1141
–1142
.325.
Phillips
A
and Lu
WY
(1984
), An experimental investigation of yield surfaces and loading surfaces of pure aluminum with stress controlled and strain controlled paths of loading
, ASME J. Eng. Mater. Technol.
, 106
, 349
349
.326.
Ohashi
Y
, Kawai
M
, and Kaito
T
(1985
), Inelastic behavior of type 316 stainless steel under multiaxial nonproportional cyclic stressings at elevated temperature
, ASME J. Eng. Mater. Technol.
, 107
, 101
101
.327.
Stout
MG
, Matin
PL
, Helling
DE
, and Canova
GR
(1985
), Multiaxial yield behavior of 1100 aluminum following various magnitudes of prestrain
, Int. J. Plast.
, 1
, 163
163
.328.
Tokuda
M
, Kratochvil
J
, and Ohno
N
(1986
), Inelastic behavior of polycrystallin metals under complex loading condition
, Int. J. Plast.
, 1
, 141
141
.329.
Ohnami
M
, Sakane
M
, and Nishino
S
(1988
), Cyclic behavior of a type 304 stainless steel in biaxial stress states at elevated temperatures
, Int. J. Plast.
, 4
, 77
77
.330.
Gou
WS
(1989
) Research on yield condition of engineering materials (in Chinese
), Sci. Sin.
, 32
(5
), 554
–559
.331.
Ikegami K (1989), Experimental plasticity of metals at low temperature: A brief review, Advance in Constitutive Laws for Eng. Material, Int. Acad. Publ., 78–84.
332.
Kim
KT
and Suh
J
(1989
), Elasto-plastic strain hardening response of porous metals
, Int. J. Eng. Sci.
, 27
, 767
–778
.333.
Zbib
HM
and Aifantis
EC
(1989
), A gradient-dependent theory of plasticity: Application to metal and solid instabilities
, Appl. Mech. Rev.
, 42
(11
, Pt2), 295
–304
.334.
Wu
HC
and Yeh
WC
(1991
), On the experimental determination of yield surface and some results of annealed 304 stainless steel
, Int. J. Plast.
, 7
, 803
803
.335.
Gologanu
M
et al. (1993
), Approximate models for ductile metals containing non-spherical voids-case of asisymmetric prolate ellipsoidal cavities
, J. Mech. Phys. Solids
, 41
, 1723
–1754
.336.
Hilinski EJ, Lewandowski JJ, and Want PT (1996), In: Aluminum and Magnesium for Automotive Applications, JD Bryant (ed), 189, Warrendale, PA, TMS-AIME.
337.
Babel
HW
, Eitman
DA
, and Mclver
RW
(1967
), The biaxial strengthening of tectured titanium
, ASME Trans.
, D89
(1
), 13
–18
.338.
Crosby
JR
, Burns
DJ
, and Benham
PP
(1969
), Effect of stress biaxiality on the high-strain fatigue behaviour of an aluminium copper alloy
, J. Experimental Mech.
, 9
(3
), 305
–312
.339.
Szczepinski
W
and Miastkowski
J
(1968
), An experimental study of the effect of the prestressing history on the yield surfaces of an aluminium alloy
, J. Mech. Phys. Solids
, 16
(3
), 153
–162
.340.
Phillips A (1970), Yield surfaces of pure aluminium at elevated temperatures, Proc. IUTAM Symp Thermoinelasticity, 241–258.
341.
Smith
S
and Almroth
BO
(1970
), An experimental investigation of plastic flow under biaxial stress
, Exp. Mech.
, 10
(6
), 217
–224
.342.
Williams
JF
and Svensson
NL
(1970
), Effect of tensile prestrain on yield locus of 1100-F aluminium
, J. Am. Stat. Assoc.
, 5
, 128
128
.343.
Hecker
SS
(1971
), Yield surfaces in prestrained aluminum and copper
, Metall. Trans.
, 2
, 2077
2077
.344.
Hecker
SS
(1972
), Experimental investigation of corners in the yield surface
, Acta Mech.
, 13
, 69
–86
.345.
Ellison
EG
and Andrew
JMH
(1973
), Biaxial cycle high strain fatigue of aluminium alloy RR58
, J. Strain Anal.
, 8
(3
), 209
–219
.346.
Hurst RC (1984), The influence of multiaxiality of stress and environmental induced degration on the creep behaviour of alloy 800H tubular component, Mechanical Behavour of Materials-4 (ICM-4), J Carlsson and NG Ohlson (eds) Pergamon Press, 1, 199–205.
347.
Helling
DE
, Miller
AK
, and Stout
MG
(1986
), An experimental investigation of the yield loci of 1100-0 aluminum, 30 brass and an overaged 2024 aluminum alloy after various prestrains
, ASME J. Eng. Mater. Technol.
, 108
, 313
313
.348.
Lee
JH
(1988
), Some exact and approximate solutions for the modified von Mises criterion
, ASME J. Appl. Mech.
, 55
, 260
–266
.349.
Shang DG and Yao WX (1998), Description of multiaxial cyclic stress-strain relationship with a simple approach, Strength Theory, Science Press, Beijing, New York, 761–766.
350.
Granlund
J
and Olsson
A
(1998
), Modelling of the plastic behaviour of structural steel based on biaxial testing
, J. Cnstruct Steel Res.
, 46
(1–3
), 404
–405
.351.
Bao YW and Steinbrech RW (1998), Strength behavior and failure criterion of brittle materials under biaxial stresses, Strength Theory, Science Press, Beijing, New York, 169–174.
352.
Collins IF (1998), An alternative approach to the formulation of strength criteria for elastic-plastic materials, Strength Theory, Science Press, Beijing, New York, 883–888.
353.
An
M
(1991
), Introduction of the twin shear strength theory and its application (in Chinese
), Hydroelec J. Northwest China
, 9
(3
), 35
–40
.354.
Steinmann
P
and Willam
K
(1994
), J. Eng. Mech. Div.
, 120
, 2428
2428
.355.
Wang
CH
and Brown
MW
(1994
), A study of the deformation behavior under multiaxial loading
, Eur. J. Mech. A/Solids
, 13
, 175
175
.356.
Hopperstad
OS
, Langseth
M
, and Remseth
S
(1995
), Cyclic stress-strain behaviour of alloy AA6060 T4, Part 2: Biaxial experiments and modelling
, Int. J. Plast.
, 11
, 741
741
.357.
Lu MS, Goto SJ, Liu W, Aso S, and Koamtsu Y (1998), A model based high-temperature deformation for precipitation hardened alloy, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds) Science Press, Beijing, New York, 145–150.
358.
Maeda
Y
, Yanagawa
F
, Barlat
F
et al. (1998
), Experimental analysis of aluminum yield surface for binary Al-Mg alloy sheet samples
, Int. J. Plast.
, 14
(4
), 301
–318
.359.
Wei ZG, Hu SS, Li YC, and Tang ZP (1998), Adiabatic shear failure of pre-torqued tungsten heavy alloy under combined dynamic compression/ shear loading, Strength Theory, Science Press, New York, 477–482.
360.
Takagi
J
and Shaw
MC
(1983
), Brittle failure initiation under complex stress state
, ASME J. Eng. Ind.
, 105
, 143
143
.361.
Bryant JD (ed) (1996), Aluminum and Magnesium for Automotive Applications, Warrendale PA, TMS-AIME.
362.
Brunig
M
, Berger
S
, and Obrecht
H
(2000
), Numerical simulation of the localization behavior of hydrostatic-stress-sensitive metals
, Int. J. Mech. Sci.
, 42
(11
), 2147
–2166
.363.
Osaki SH and Iino M (1998), Stress corrosion cracking behaviors of high-strength aluminum alloys under complex stress state, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 817–822.
364.
Chung
JS
(ed) (1987
), Ice mechanics
, Appl. Mech. Rev.
, 40
(9
), 1191
–1244
.365.
Kerr
AD
(1976
), Bearing capacity of floating ice plates subjected to static or quasi-static loads—A critical survey
, J. Glaciology
17
, 43
43
.366.
Dempsey JP and Rajapakse Y (eds) (1995), Ice Mechanics, ASME AMD 207, New York.
367.
Szyszkowski
W
and Glockner
PG
(1985
), A nonlinear constitutive model for ice
, Int. J. Solids Struct.
, 21
, 307
–321
.368.
Szyszkowski
W
and Glockner
PG
(1986
), On a multiaxial constitutive law for ice
, Mech. Mater.
, 5
, 49
–71
.369.
Mahrenholtz O, Palathingal P, and Konig JA (1989), The behaviour of ice in the two-dimensional stress state, Advance in Constitutive Laws for Eng. Material, Int Acad Publ, 106–110.
370.
Chen
ZP
and Chen
SH
(1999
), The ice load on cone (English Abstract
), Engineering Mechanics
, 16
(6
), 82
–92
.371.
Beltaos
S
(1978
), Strain energy criterion for failure of floating ice sheets
, Canadian J. Civil Eng.
5
, 352
–361
.372.
Coon MD, Evans RJ, and Gibson DH (1984), Failure criteria for sea ice and loads resulting from crushing, Proc of IAHR Int Symp on Ice Problems.
1.
Bazant
ZP
and Kim
JJH
(1998
), Size effect in penetration of sea ice plate with part-through cracks, (1) Theory; (2) Results, J. Eng. Mech.
, 124
(12
), 1310
–1315
2.
124
(12
), 1316
–1324
.1.
Bazant
ZP
and Chen
EP
(1997
), Scaling of structural failure
, Appl. Mech. Rev.
, 50
(10
), 593
–627
.2.
Cole DM (1988), Strain energy failure criterion for S2 fresh water ice in flexure, Proc IAHR Int Symp on Ice Problems, 1.
3.
Tryde P (ed) (1980), IUTAM Symposium on the Physics and Mechanics of Ice, Springer-Verlag, Berlin.
4.
Hibler
WD
(1979
), A dynamic thermodynamic sea ice model
, J. Phys. Oceanogr.
, 9
(44
), 815
–846
.5.
Sodhi
DS
(1995
), Breakthrough loads of floating ice sheets
, J Cold Regions Engrg
, 9
(1
), 4
–22
.6.
Gol’dshtein
RV
and Marchenko
AV
(1999
), The choice of constitutive relations for an ice cover
, J. Appl. Math. Mech.
, 63
(1
), 73
–78
.7.
Gutfraind
R
and Savage
SB
(1998
), Marginal ice zone rheology: comarison of results from continuum-plastic models and discrete-particle simulations
, Oceanog Lit Rev
, 45
(1
), 29
29
.8.
Schulson
EM
and Gratz
ET
(1999
), The brittle compressive failure of orthortropic ice under triaxial loading
, Acta Mater.
, 47
(3
), 745
–755
.9.
Dempsey
JP
(2000
), Research trends in ice mechanics
, Int. J. Solids Struct.
, 37
, 131
–153
.10.
Whitney
W
and Andres
RD
(1967
), The behaviour of polystyrene, polymrthl, methacrylate, polycarbonate, and polyvinyl formale under conplex stress state
, J. Polym. Sci.
, 16
, 2961
2961
.11.
Sternstein
SS
and Ongchin
L
(1969
), Amer Chem Polymer
, 10
, 1117
1117
.12.
Oxborough
RJ
and Bowder
PB
(1973
), Philos. Mag.
, 28
, 547
547
.13.
Raghava
R
et al. (1973
), Macroscopic yield criterion for crystalline polymers
, Int. J. Mech. Sci.
, 15
(12
), 967
–974
.14.
Matsushige
K
, Radcliffe
SV
and Bear
E
(1974
), J. Mater. Sci.
, 10
, 833
833
.15.
Sternstain
SS
and Myers
FA
(1973
), Yielding of glassy polymers in the second quadrant of principal stress space
, J. Macromol. Sci., Phys.
, B8
, 537
–571
.16.
Bowder
PB
and Jukes
JA
(1972
), Plastic flow of polymers
, J. Mater. Sci.
, 7
, 52
–63
.17.
Bowder PB (1973), The yield behavior of glassy polymers, The Physics of Glassy Polymers, RN Haward (ed), Ch 5 Wiley, New York, 279–389.
18.
Argon
AS
and Bessonor
MI
(1977
), Plastic flow in glassy polymers
, Polym. Eng. Sci.
, 17
(3
), 174
–182
.19.
Argon
AS
and Hannoosh
JG
(1977
), Initiation of crazing in polymers
, Philos. Mag.
, 36
, 1217
–1234
.20.
Argon AS, Hannoosh JG, and Salama MM (1977), In Fracture, 1, Waterloo, 445.
21.
Malmeisters AK, Tamuz VP, and Teters GA (1980), Resistance of Polymer and Composite, Chapter 3, Strength theory (in Russian), Zunatne, 233–319.
22.
Tamuzs VP (1981), Theory of scattered fracture at the complex stress state, Fracture Micromechanics of Polymer Materials, VS Kuksenko and VP Tamuzs (eds), Martinus Nijhoff Publ, Boston, Ch 8, 189–253.
23.
van der Giessen
E
and Tvergarrd
V
(1989
), A creep rupture model accounting for cavitation at sliding grain boundaries
, Int. J. Fract.
, 48
, 153
–175
.24.
Zhu
XX
(1992
), Yielding and plastic deformation of solid polymers (in Chinese
), Advances in Mechanics
, 22
(4
), 449
–463
.25.
Zhu XX and Zhu GR (1992), Strength of Polymers (in Chinese), Zhejiang Univ Press, Hanzhou, 431 pp.
26.
Wu PD and Giessen E (1994), Constitutive Modelling of the Large Strain Behavior of Rubbers and Amorphous Glassy Polymers, Delft Univ of Technology, Delft.
27.
Estevez
R
, Tijssens
MGA
, and van der Giessen
E
(2000
), Modeling of the competition between shear yielding and crazing in glassy polymers
, J. Mech. Phys. Solids
, 48
(12
), 2585
–2617
.28.
Tijssens
MGA
, van der Giessen
E
, and Sluys
LJ
(2000
), Modeling of crazing using a cohesive surface methodology
, Mech. Mater.
, 32
(1
), 19
–35
.29.
Jones JW and Knauss WG (1965), In AIAA Solid Propellant Rocket Conf 6th, Paper No. 65–157.
30.
Kruse RB and Jones TM (1965), In AIAA Solid Propellant Rocket Conf 6th, Paper No. 65–156.
31.
Zak AR (1964), SPIA Publ 61U501.
32.
Darwell HM, Parker A, and Leeming H (1965), In AIAA Solid Propellant Rocket Conf 6th, Paper 65–161.
33.
Sharma MG (1965), SPIA Publ. 94,297.
34.
Sharma MG and Lim CK (1966), SPIA, Publ. 119,1,625.
35.
Swanson
SR
and Christenson
LW
(1980
), A constitutive formulation for high elongation propellants
, J. Spacecraft
, 20
, 559
–566
.36.
Finne S, Futsaether C, and Botnan JI (1990), Three analysis of solid propellant grain using a nonlinear visco-elastic model, AIAA-2029, 1–8.
37.
Shen
HR
(1992
), Creep damage model of solid propellant coupled with temperature phase (in Chinese
), J. of Solid Rocket Technology
, 11
(4
), 39
–43
.38.
Xie
RH
and Tang
YH
(1992
), Specimen study for complex stress testa of composite plates (in Chinese
), J. of Solid Rocket Technology
, 11
(4
), 82
–97
.39.
Qiang HF, Yu MH, and Qu WZ (1998), Twin-shear unified elasto-visco-plasticity constitutive model and its finite element analysis, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 917–924.
40.
Qiang HF (1999), Numerical analysis and experimental researches on solid rocket motor grain structure integrrity, PhD Thesis, Xi’an Jiaotong.
41.
Pinto
J
and Weigand
DA
(1991), The mechanical response of TNT and a composite of TNT and RDX to compressive stress: II. Triaxial stress and yield, J. Engrg. Mater. (9), 205–263.42.
Zhang YC, Yin M, Han XP, and Shen YP (1998), A computer numerical method for determine energetic materials mechanical response to a confined triaxial dynamic compression, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 643–648.
43.
Broutman
LJ
and Cornish
RH
(1965
), Effect of polyaxial stress on failure strength of alumina ceramics
, J. Am. Ceram. Soc.
, 48
, 519
–524
.44.
Richard E (1965), J. Am. Ceram. Soc., 48(10).
45.
Adams
M
and Sines
G
(1976
), Determination of biaxial compressive strength of a sintered alumina ceramic
, J. Am. Ceram. Soc.
, 59
(7–8
), 300
–304
.46.
Lamon J (1988), Ceramics reliability: Statistical analysis of multiaxial failure using the Weibull approach and the multiaxial elemental strength model, ASME-Paper No 88-GT-147.
47.
Sturmer GS, Schulz A, and Wittig S (1991), Life time prediction for ceramic gas turbine components ASME-Paper No 91-GT-96.
48.
Baker G and Karihaloo L (ed) (1994), IUTAM Symp on Fracture of Brittle, Disordered Materials: Concrete, Rock, and Ceramics, E & FN SPON, London.
49.
Rosenberg
Z
, Dekel
E
, and Hohler
V
et al. (1997
), Hypervelocity penetration of tungsten alloy rods into ceramic tiles: Experiments and 2-D simulations
, Int. J. Impact Eng.
, 20
, 675
–683
.50.
Gurney C and Rowe PW (1945), Fracture of glass rods in bending and under radial pressure, R. Aircraft Estab Rep Memo, 2284.
51.
Taylor
NW
(1947
), Mechanism of fracture of glass and similar brittle solids
, J. Appl. Phys.
, 18
, 943
–955
.52.
Davigenkov HH and Stabrokin AE (1954), Bull. Acad. Sci. USSR, Phys. Ser. (in Russian), 8.
53.
Shaw
MC
and Sata
T
(1966
), Int. J. Mech. Sci.
, 8
, 469
469
.54.
Gibson LJ, and Ashby MF (1998), Cellular Solids, Cambridge Univ Press, Cambridge.
55.
Gibson
LJ
, Ashby
MF
, Zhang
J
, Triantafillou
TC
et al. (1989
), Failure surface for cellular mateerials under multiaxial loads-(1) Modelling
, Int. J. Mech. Sci.
, 31
(9
), 635
–663
.56.
Triantafillou
TC
, Zhang
J
, Shercliff
TL
, Gibson
LJ
, and Ashby
MF
(1989
), Failure surface for cellular mateerials under multiaxial loads-(2): Comparison of models with experiment
, Int. J. Mech. Sci.
, 31
(9
), 665
–678
.57.
Triantafillou
TC
and Gibson
LJ
(1990
), Multiaxial failure criteria for brittle foams
, Int. J. Mech. Sci.
, 32
(6
), 479
–496
.58.
Deshpande
VS
and Fleck
NA
(2000
), Isotropic constitutive models for metallic foams
, J. Mech. Phys. Solids
, 48
(6–7
), 1253
–1283
.59.
Espinosa
HD
(1995
), On the dynamic shear resistance of ceramic composite and its dependence on applied multiaxial deformation
, Int. J. Solids Struct.
, 31
, 3105
3105
.60.
Theocaris
PS
(1991
), The elliptic paraboloid failure criterion for cellular solids and brittle foams
, Acta Mech.
, 89
, 93
–121
.61.
Meinecke EA and Clark RC (1973), Mechanical Properties of Polymeric Foams, Westport: Tech Publ Com Int.
62.
Badiche
X
, Forest
S
, Guibert
T
et al. (2000
), Mechanical properties and non-homogeneous deformation of open-ell nikel foams: application of the mechanics of cellular solids and of porous materials
, Mater. Sci. Eng., A
, A289
, 276
–288
.63.
Yin
M
, Li
H
, and Han
XP
(1998
), An experimental study of triaxial compressive dynamic mechanical properties of foam plastics
, J Xian Jiaotong Univ
, 32
(6
), 78
–81
.64.
Ashby MF, Evans AG, Fleck NA, Gibson LJ, Huntchinson JW, and Wadley HNC (2000), Metal Foams: A Design Guide, Butterworth Heinemann, Oxford.
65.
Gioux
G
, McCormark
TM
, and Gibson
LJ
(2000
), Failure of aluminum foams under multiaxial loads
, Int. J. Mech. Sci.
, 42
(6
), 1097
–1117
.66.
Chen
IW
and Reyes-Morel
PE
(1986
), J. Am. Ceram. Soc.
, 69
(3
), 181
–186
.67.
Huang
W
(1999
), “Yield” surfaces of shape memory alloys and their applications
, Acta Mater.
, 47
(9
), 2769
–2776
.68.
Lynch
CS
(1998
), On the development of multi-axial phenomenological constitytive laws for ferroelectric ceramics, J. Intell. Mater. Syst. Struct.
, 9
(7
), 555
–563
.69.
Huber
JE
and Fleck
NA
(2001
), Multi-axial electrical switching of a ferroellectric: theory versus experiment
, J. Mech. Phys. Solids
, 49
(4
), 785
–811
.70.
Whitfield
JK
and Smith
CW
(1972
), Characterization studies of a potential photoelastic-plastic material
, Exp. Mech.
, 12
(2
), 67
–74
.71.
Javornicky J (1974), Photoplasticity, Elsevier, Amsterdam.
72.
Zachary
BW
and Riley
WF
(1977
), Optical response and yield behavior of a polyester model material
, Exp. Mech.
, 17
(9
), 321
–326
.73.
Yin
ZX
, Zhang
SK
, Gong
YF
et al. (1995
), Further study on the principl of photoplasticity (in Chinese
), J Experimental Mech.
, 10
(2
), 252
–256
.74.
Zhu MH and Fan L (1995), Modern Photoplasticity (in Chinese), Defence Ind Press, Beijing.
75.
Cowin
SC
(1979
), On the strength anisotropy of bone and wood
, ASME J. Appl. Mech.
, 46
(4
), 832
–838
.76.
Keaveney
TM
and Wachtel
EF
(1999
), Application of the Tsai-Wu quadretic multiaxial failure criterion to bovine trabecular bone
, ASME J. Biomech. Eng.
, 121
(1
), 99
–107
.77.
Keyak
JH
and Rossi
SA
(2000
), Prediction of femoral fracture load using finite element models: An examination of stress and strain based failure theories
, J. Biomech.
, 33
(2
), 209
–214
.78.
Pietruszczak
S
, Inglis
D
, and Pande
GN
(1999
), A fabric-dependent fracture criterion for bone
, J. Biomech.
, 32
(10
), 1071
–1079
.79.
Schwaitz
FG
and Holland
AR
(1969
), Determination of yield criterion for iron powder undergoing compaction
, Int. J. Powder Metall.
, 5
, 79
–83
.80.
Shima
S
and Mimura
K
(1985
), Densification behaviour of ceramic powder
, Int. J. Mech. Sci.
, 28
, 53
53
.81.
Kuhn
HA
and Downey
CL
(1971
), Deformation characteristics and plasticity theory of sintered powder metal materials
, Int. J. Powder Metall.
, 7
, 15
–25
.82.
Shima
S
and Oyane
M
(1976
), Plasticity theory for porous metals
, Int. J. Mech. Sci.
, 18
, 285
–291
.83.
Lade PV and Mazen AA (1990), Brittle and ductile transition oat failure in frictional materials (powder metals), Micromechanics of Failure of Quasi-Brittle Materials, SP Shah, SE Swartz, and ML Wang (eds), Elsevier.
84.
Doraivelu
SM
et al. (1984
), A new yield function for compressible P/M materials
, Int. J. Mech. Sci.
, 26
, 527
–535
.85.
Gathin
DT
et al. (1994
), An investigation of powder compaction processes
, Int. J. Powder Metall.
, 30
, 385
–398
.86.
Sano T, Sukegawa N, Takeishi H, and Horikoshi (1998), Malvern-Type Constitutive Equation for Dynamic Powder Compaction, Strength Theory, Science Press, Beijing, New York, 55–60.
87.
Akisanya
AR
, Cocks
ACF
, and Fleck
NA
(1997
), The yield behaviour of metal powders
, Int. J. Mech. Sci.
, 39
(12
), 1315
–1324
.88.
Khoei
AR
and Lewis
RW
(1998
), Finite element simulation for dynamic large elasto-plastic deformation in metal powder forming
, Finite Elem. Anal. Design
, 30
, 335
–352
.89.
Park
SJ
, Han
HN
et al. (1999
), Model for compaction of metal powder
, Int. J. Mech. Sci.
, 41
(1
), 121
–141
.90.
Sridhar
I
and Fleck
NA
(2000
), Yield behaviour of cold compacted composite powders
, Acta Mater.
, 48
(13
), 3341
–3352
.91.
Henderson
RJ
, Chandler
HW
, Akisanya
AR
et al. (2001
), Micro-mechanical modelling of powder compaction
, J. Mech. Phys. Solids
, 49
(4
), 739
–759
.92.
Narayanasamy
R
et al. (2001
), Generalized yield criteria of porous sintered powder metallurgh metals
, J. Mater. Process. Technol.
, 110
(2
), 182
–185
.93.
Diao
DF
(1999
), Finite element analysis on local map and critical maximum contact pressure by yielding in hard coating with an interlayer under sliding contact
, Tribol. Int.
, 32
(1
), 25
–32
.94.
Wang
CH
and Chalkley
D
(2000
), Plastic yielding of a film adhesive under multiaxial stresses
, Int. J. of Adhesion and Adhesives
, 20
(2
), 155
–164
.95.
Alexandrov
S
and Richmond
O
(2000
), On estimating the tensile strength of an adhesive plastic layer of arbitrary simply connected contor
, Int. J. Solids Struct.
, 37
(4
), 669
–686
.96.
Sheppard
A
, Kelly
D
, and Tong
L
(1998
), A damage zone model for the failure analysis of adhesively boned joints
, J Adhesion and adhesive
, 18
(6
), 385
–400
.97.
Ishii
K
, Imanaka
M
, Nakayama
N
et al. (1998
), Fatigue failure criterion of adhesively bonded CFRP/metal joint under multiaxial stress conditions
, Composites Part A: Appl Sci and Manuf
29
(4
), 415
–422
.98.
National Bureau of Standards (1983), Mechanical Properties, Performance, and Failure Modes of Coating, Proc of the 37th Meeting of the Mechanical Prevention Group.
99.
Zhang
DQ
, Xu
KW
, and He
JW
(1991
), Aspects of the residual stress field at a notch and its effect on fatigue
, Mater. Sci. Eng., A
, A136
, 79
–83
.100.
Lee
YK
, Ghosh
J
, Bair
S
, and Winer
W
(1994
), Shear band analysis for lubricants based on a viscoelastic plasticity model
, Appl. Mech. Rev.
, 47
(6
), S209–S220
S209–S220
.101.
Aubertin
M
, Dill
DE
, and Ladanyi
B
(1994
), Constitutive equations with internal state variables for the inelastic behavior of soft rocks
, Appl. Mech. Rev.
, 47
(6
, Pt 2), S97–S101
S97–S101
.102.
Hobbs
DW
(1962
), The strength of coal under biaxial compression
, Colliery Eng
, 39
, 285
–290
.103.
Hobbs
DW
(1964
), The strength and stress-strain characteristics of Oakdale coal in triaxial compression
, J. Geol.
, 72
, 214
–231
.104.
Medhurst
TP
and Brown
ET
(1998
), A study of the mechanical behaviour of coal for pillar design
, Int. J. Rock Mech. Min. Sci.
, 35
(8
), 1087
–1105
.105.
de Buhan
P
and de Pelice
G
(1997
), A homogenization approach to the ultima- te strength of brick masonry
, J. Mech. Phys. Solids
, 45
(7
), 1085
–1104
.106.
Lotfi
HR
and Shing
PB
(1994
), An interface model applied to fracture of masonry structures
, J. Struct. Div. ASCE
, 120
(1
), 63
–80
.107.
Lotfi
HR
and Shing
PB
(1991
), An appraisal of smeares crack models for masonry shear wall analysis
, Comput. Struct.
, 41
(3
), 413
–425
.108.
Sabhash
AC
and Kishore
YK
(1996
), Three-dimensional failure analysis of composite massonry walls
, J. Struct. Div. ASCE
, 122
(9
), 1031
–1040
.109.
Sinha
BP
and Ng
CL
(1997
), Failure criterion and behavior of brickwork in biaxial bending
, J. Mater. in Civil Engrg.
, 9
(2
), 70
–75
.110.
Bull JW (ed) (2000), Computational Modelling of Masonry, Brickwork, and Blockwork Structures, Saxe-Coburg Publ, Edinburgh.
1.
Eid
HT
, Stark
TD
, and Evans
WD
et al. (2000
), Municipal solid waste slope failure. I: Waste and fundation soil properties; II: Stability analyses
, J. Geotech. Eng.
, , 126
(5
), 408
–419
2.
126
(5
), 408
–419
.1.
Randolph
MF
and Wroth
CP
(1981
), Application of the failure state in undrained simple shear to the shaft capacity of driven piles
, Geotechnique
, 31
(1
), 143
–157
.2.
Baker
R
and Desai
CS
(1982
), Consequences of deviatoric normality in plasticity with isotropic strain hardening
, Int. J. Numer. Analyt. Meth. Geomech.
, 6
(3
), 383
–390
.3.
Desai
CS
, Somasundaram
S
, and Frantziskonis
G
(1986
), A hierachical approach for constitutive modelling of geological material
, Int. J. Numer. Analyt. Meth. Geomech.
, 10
(3
), 201
–212
.4.
Tun ZL, Hasegawa T, and Thai NC (1998), Numerical simulation of flow deformation behaviour of two and three phase porous media, Strength Theory, Science Press, Beijing, New York 615–620.
5.
Khan AS and Huang S (1995), Continuum Theory of Plasticity, Wiley, New York.
6.
Kolymbas
D
, Herle
I
, and von Wolffersdorff
PA
(1995
), (PAPER TITLE?) Int. J. Numer. Analyt. Meth. Geomech.
, 19
, 415
–436
.7.
Zienkiewicz
OC
and Huang
MS
(1995
), (PAPER TITLE?) Int. J. Numer. Analyt. Meth. Geomech.
, 19
, 127
–148
.8.
Fotiu PA and Ziegler F (1995), Constitutive modelling of porous viscoplastic solids, Beitrage zur Mechanik (Festschrift Zum 60. Geburtstag von Prof. Dr.-Ing.Reint de Boer), 91–100.
9.
Fang DN, Lu W, and Hwang KC (1998), Investigation on CuAlNi single crystal: Behavior of deformation and growth of martensite under biaxial loading, Strength Theory, Science Press, Beijing, New York, 521–528.
10.
Kou SQ, Zhang ZX, Lindqvist PA et al. (1998), Interaction between a growing crack and a grain, Strength Theory, Science Press, Beijing, New York, 603–608.
11.
Sugiyama M, Wakun I, Tonosaki A, and Akaishi M (1998), Ratio of undrained shear strength to vertical effective stress, Strength Theory, Science Press, Beijing, New York, 271–278.
12.
Fridman YB (1946), Mechanical Properties of Materials (in Russian), Oborongiz, Moscow.
13.
Fridman YB (1943), United Strength Theory of Materials (in Russian), Oborongiz, Moscow.
14.
Encyclopedia of China (1985), Mechanics, China Encyclopedia Press, Beijing.
15.
Desai CS and Wathugala GW (1987), Hierarchical and unified models for solids and discontinuities, Implementation of Constitutive Laws for Engineering Materials (2nd Int Conf on Constitutive Laws for Eng. Materials), CS Desai et al. (eds).
16.
Valliappans S and Yazdchi M (1998), Damage mechanics as a unified strength theory, Strength Theory, Science Press, Beijing, New York, 79–88.
17.
Yu
MH
and He
LN
(1991
), The historical evolution and recent development of the strength theory in the field of strength of materials (in Chinese
), Mech. Pract.
, 13
(2
), 59
–61
.18.
Yu
MH
(1994
), Unified strength theory for geomaterials and its application (English Abstract
), Chin J. Geotech Eng.
, 16
(2
), 1
–9
.19.
Yu
MH
and Zeng
WB
(1994
), New theory of engineering structural analysis and its application (English abstract
), Eng. Mech.
, 11
(1
), 9
–20
.20.
Yu
MH
, Yang
SY
, Liu
CY
, and Liu
JY
(1997
), Unified plane-strain slip line system (in Chinese
), Chin. Civil Eng. J.
, 30
(2
), 14
–26
.21.
Yu
MH
, Zhang
YQ
, and Li
JC
(1998
), Another important generalization of the unified strength theory (in Chinese
), J Xi’an Jiaotong Univ
, 32
(12
), 108
–110
.22.
Yu
MH
, Zhang
YQ
, and Li
JC
(1999
), The unified characteristic line for plastic plane stress problems (English Abstract
), J Xi’an Jiaotong Univ
, 33
(4
), 1
–4
.23.
Yu
MH
, Li
JC
, and Zhang
YQ
(2001
), Unified characteristics line theory of spacial axisymmetric plastic problem
, Sci. China, Ser. E: Technol. Sci.
, 44
(2
), 207
–215
.24.
Liu
SY
(1997
), Generalized twin shear unified strength theory and its application (in Chinese
), J. Hydraul. Eng.
, 42
(4
), 72
–78
.25.
Yu
MH
et al. (1998
), Constitutive model: From single shear to tri-shear to twin-shear to unification (English Abstract
), Chin J. Rock Mech. Eng.
, 17
(Suppl), 739
–743
.26.
Yu
MH
, Yang
SY
, Fan
SC
et al. (1997
), Twin shear unified elasto-plastic constitutive model and its applications (in Chinese
), Chin. J. Geotech. Eng.
, 21
(6
), 9
–18
.27.
Qiang
HF
and Lu
N
(1999
), Unified solution of crack tip plastic zone under small scale yielding
, Chin. J. Mech. Engrg.
, 35
(1
), 34
–38
.28.
Song
L
and Yu
MH
(1998
), Unified Elasto-plastic analysis of pressure tunnel (English Abstract
), Eng. Mech.
, 15
(4
), 57
–61
.29.
Fan
SC
, Yu
MH
, and Yang
SY
(2001
), On the unification of yield criteria
, ASME J. Appl. Mech.
, 68
(2
), 341
–343
.30.
Zhang
YQ
, Song
L
, and Fan
W
(1998
), Unified slip line solution of the wedge’s ultimate load and its application in geotechnical engineering (in Chinese
), J Xi’an Jiaotong Univ.
, 32
(12
), 59
–62
.31.
Yu
MH
, Yang
SY
, and Fan
SC
(1999
), Unified elasto-plastic associated and non-associated constitutive model and its application
, Comput. Struct.
, 71
(6
), 627
–636
.32.
Li
JC
, Yu
MH
, and Fan
SC
(2000
), A unified solution for limit load of simply-supported oblique plates, rhombus plates, rectangle plates, and square plates (English Abstract
), Chin. Civil Eng. J.
, 33
(6
), 76
–80
.33.
Li JC, Yu MH, and Gong YN (2000), Dynamic investigation of semi-infinite concrete target penetrated by long rod, Proc of 3rd Asian-Pacific Conf on Aerospace Technology and Science, YN Gong and PQ Liu (eds), Beijing Univ. of Aeronaut and Astronaut, 263–270.
34.
Zhang
YQ
, Li
JC
, and Liao
HJ
(1999
), Unified ultimate solution of a large thin plane with a hole
, J. Mechanical Strength
, 21
(1
), 45
–47
.35.
Liao
HJ
, Han
B
, Ding
CH
et al. (2001
), Determination of effective dynamic strength index of soils under complex stress
, J. Xi’an Jiaotong Univ.
, 35
(5
), 532
–539
.36.
Hill
R
(1948
), Theory of yield and plastic flow of anisotropic metals
, Proc. Royal Society
, A193
, 281
–297
.37.
Hu
LW
and Marin
J
(1955
), Anisotropic loading functions for combined stress in the plastic range
, ASME J. Appl. Mech.
, 22
(1
), 77
–81
.38.
Marin
J
(1956
), Theories of strength for combined stresses and nonisotropic materials
, J. Aeronaut. Sci.
, 24
(4
), 265
–269
.39.
Marin
J
and Sauer
JA
(1957
), Theories of strength for combined stresses and nonisotropic materials
, J. Aeronaut. Sci.
, 24
(4
), 265
–268
.40.
Hu
LW
(1958
), Modified Tresca’s yield condition and associated flow rule for anisotropic materials and its applications
, J. Franklin Inst.
, 265
, 187
–204
.41.
Griffith
JE
and Baldwin
WM
(1962
), Failure theories for generally orthotropic materials
, Developments of Theor. & Appl. Mech.
, 1
, 410
–420
.42.
Smith
GF
(1962
), On the yield condition for anisotropic materials
, Q. Appl. Math.
, 20
(3
), 241
–247
.1.
Goldenblat
Il
and Kopnov
VA
(1965
), Strength criterion of anisotropic materials (in Russian
), Bull. Acad. Sci. USSR, Phys. Ser. (Engl. Transl.)
, 6
, 77
–83
; 2.
Polymer Mech.
, 1
(2
), 70
–78
.1.
Ashkenazi
EK
(1965
), Problems of the anisotropy of strength (in Russian
), Polymer Mech.
, 1
(2
), 79
–92
.2.
Azzi
VD
and Tsai
SW
(1965
), Anisotropic strength of composites
, Exp. Mech.
, 5
(9
), 283
–288
.3.
Hsu
TC
(1966
), A theory of the yield and flow rule of anisotropic materials
, J. Strain Anal.
, 1
(3
), 204
–215
.4.
Franklin
HG
(1968
), Classic theory of failure of anisotropic materials
, Fibre Sci. Technol.
, 1
(2
), 137
–150
.5.
Bastun
VN
and Chernyak
NI
(1966
), On application of some yield conditions for anisotropic steel (in Russian
), Prykladna Mekh
, 5
(2
), 135
–138
.6.
Malmeister
AK
(1966
), Geometry of theories of strength (in Russian
), Polym Mech
, 2
(4
), 519
–534
.7.
Capurso
M
(1967
), Yield conditions for incompressible isotropic and orthotropic materials with different yield stress in tension and compression
, Meccanica
, 2
(2
), 118
–125
.8.
Hoffman
O
(1967
), The brittle strength of orthotropic materials
, J. Compos. Mater.
, 1
, 200
–206
.9.
Petit
PH
and Waddoups
ME
(1968
), A method of predicting the nonlinear behavior of laminated composites
, J. Compos. Mater.
, 3
, 2
–9
.10.
Chamis CC (1969), Failure criteria for filamentary composites, Composite Materials: Testing and Design, ASTM STP 460, 336–351.
11.
Morris
GA
and Fenves
SJ
(1969
), Approximate yield surface equations
, J. Eng. Mech. Div.
, 95
(4
), 937
–954
.12.
Neuber
H
(1969
), Anisotropic nonlinear stress-strain laws and yield condition
, Int. J. Solids Struct.
, 5
(12
), 1299
–1310
.13.
Prager
W
(1969
), Plastic failure of fiber-reinforced materials
, ASME J. Appl. Mech.
, E36
(3
), 542
–544
.14.
Shiratori
E
and Ikegami
K
(1969
), Studies of the anisotropic yield condition
, J. Mech. Phys. Solids
, 17
(6
), 473
–491
.15.
Lance
RH
and Robinson
DN
(1971
), A maximum shear stress theory of plastic failure of fiber reinforced materials
, J. Mech. Phys. Solids
, 19
(2
), 49
–60
.16.
Helfinstine
JD
and Lance
R
(1972
), Yielding of fiber reinforced Tresca material
, J. Eng. Mech. Div.
, 98
(4
), 849
–866
.17.
Lin
TH
, Salinas
D
, and Ito
YM
(1972
), Initial yield surface of a unidirectionally reinforced composite
, ASME J. Appl. Mech.
, E39
(2
), 321
–326
.18.
McLaughlin
PV
(1972
), Plastic limit behavior and failure of filament reinforced materials
, Int. J. Solids Struct.
, 8
(11
), 1299
–1318
.19.
Puppo
AH
and Evensen
HA
(1972
), Strength of anisotropic materials under combined stresses
, AIAA J.
, 10
(4
), 468
–474
.20.
Chou
PC
, McNamee
BM
, and Chou
DK
(1973
), The yield criterion of laminated media
, J. Compos. Mater.
, 7
(1
), 22
–35
.21.
O’Donnell
WJ
and Porowski
J
(1973
), Yield surfaces for perforated materials
, ASME J. Appl. Mech.
, 40
(1
), 263
–270
.22.
Dvorak
GJ
, Rao
MSM
, and Tarn
JQ
(1973
), Yielding in unidirectional composites under external loads and temperature changes
, J. Compos. Mater.
, 7
(2
), 194
–216
.23.
Dvorak
GJ
, Rao
MSM
, and Tarn
JQ
(1974
), Generalized initial yield surfaces for unidirectional composites
, ASME J. Appl. Mech.
, E41
(1
), 249
–253
.24.
Dvorak GJ and Bahei-El-Din A (1997), Inelastic composite materials: Transformation analysis and experiments, Continuum Micromechanics, P Suque (ed), Springer, Wien, 1–60.
25.
Bastun
VN
(1974
), On the yield condition of an anisotropically hardening material (in Russian
), Strength Prob
, 2
, 88
–96
.26.
Tennyson
RC
, MacDonald
D
, and Nanyaro
AP
(1978
), Evaluation of the tensor polynomial failure criterion for composite materials
, J. Compos. Mater.
, 12
, 63
–75
.27.
Daniel
IM
(1982
), Biaxial testing of [0/45] graphite epoxy plates with holes
, Exp. Mech.
, 5
, 156
–160
.28.
Soni SR (1983) Stress and strength analysis of composite laminates at delamination, Progress in Science and Engineering of Composites, Proc of 4th Conf on Composite Materials, 1982, 1, 251–260.
29.
Liu
JY
(1984
), Evaluation of the tensor polynomial strength theory for wood
, J. Compos. Mater.
, 18
(3
), 216
–226
.30.
Tsai
SW
(1984
), A survey of macroscopic failure criteria for composite materials
, J. Reinf. Plast. Compos.
, 3
(1
), 40
–62
.31.
Sih GC and Skudra AM (ed) (1985), Failure Mechanics of Composites, Elsevier Science Pub.
32.
Bassani
JL
(1977
), Yield characterisation of metals with transversely isotropic plastic properties
, Int. J. Mech. Sci.
, 19
, 651
651
.33.
Budiansky B (1984), Anisotropic plasticity of plane-isotropic sheets, Mechanics of Material Behavior, GJ Dvorak and RT Shield (eds), Elsevier, Amsterdam, 15–29.
34.
Theocaris
PS
(1989
), The parabolic failure surface for the general orthotropic material
, Acta Mech.
, 79
, 53
–79
.35.
Aboudi
J
(1989
), Micromechanical analysis of composites by the method of cells
, Appl. Mech. Rev.
, 47
(7
), 193
–221
.36.
Voyiadjis
GZ
and Thiagarajan
G
(1995
), An anisotropic yield surface model for directionally reinforced metal-matrix composite
, Int. J. Plast.
, 11
(8
), 867
–894
.37.
Lissenden
CJ
and Arnold
SM
(1997
), Theoretical and experimental considerations in represennting macroscale flow/damage surfaces for metal matrix composites
, Int. J. Plast.
, 13
(4
), 327
–358
.38.
Valeva V and Ivanova J (1998), Strength numerical analysis of a composite material with holes, Strength Theory, Science Press, Beijing, New York, 359–364.
39.
Xu
SG
and Weinmann
KJ
(1998
, 2000), Prediction of forming limit curves of sheet metals using Hill’s 1993 user-friendly yield criterion of anisotropic materials
, Int. J. Mech. Sci.
40
(9
), 913
–925
, 42(4), 677–692.40.
Vial-Edwards
C
(1997
), Yield loci of FCC and BCC sheet metals
, Int. J. Plast.
, 13
(5
), 521
–531
.41.
Cazacu
O
and Cristescu
ND
(1999
), A parboiled failure surface for transversely isotropic materials
, Mech. Mater.
, 31
, 381
–393
.42.
Foguet
P
and Huerta
A
(1999
), Plastic flow potential for cone region of MRS- Lade model
, J. Eng. Mech. Div.
, 125
(3
), 364
–366
.43.
Maniatly
AM
, Yu
JS
et al. (1999
), Anisotropic yield criterion for polycrystalline metals using texture crystal symmetries
, Int. J. Solids Struct.
, 36
(35
), 5331
–5355
.44.
Wellerdick-Wojtasik
N
(1999
), Micromechanical modelling of yield loci
, Comput. Mater. Sci.
, 16
(1–4
), 113
–119
.45.
Cao
J
, Yao
N
, Karafillis
A
, and Boyce
MC
(2000
), Prediction of localized thinning in sheet metal using a general anisotropic yield criterion
, Int. J. Plast.
, 16
(9
), 1105
–1129
.46.
Kojic
M
, Grujovic
N
, Slavkovicb
R
, and Zivkovic
M
(1996
), A general orthotropic von Mises plasticity material model with mixed hardening: Model definition and implicity stress integration procedure
, ASME J. Appl. Mech.
, 63
(2
), 376
–382
.47.
Hashin
Z
(1980
), Failure criteria for unidirectional fiber composites
, ASME J. Appl. Mech.
, 47
, 329
–334
.48.
Dano
ML
, Gendron
G
, and Picard
A
(2000
), Stress and failure analysis of mechanically fastened joints in composite laminates
, Comput. Struct.
, 50
, 287
–296
.49.
Spottswood
SM
and Palazotto
AN
(2001
), Progressive failure analysis of a composite shell
, Comput. Struct.
, 53
, 117
–131
.50.
Hashin
Z
(1962
), The elastic moduli of heterogeneous materials
, ASME J. Appl. Mech.
, 29
, 143
–150
.51.
Ferron
G
, Makkouk
R
, and Morreale
J
(1994
), A parametric description of orthotropic plasticity in metal sheets
, Int. J. Plast.
, 10
, 431
–449
.52.
Moreira
LP
, Ferron
G
, and Ferran
G
(2000
), Experimental and numerical analysis of the cup drawing test for orthotropic metal sheets
, J. Mater. Process. Technol.
, 108
, 78
–86
.53.
Wagoner
RH
(1981
), Comparison of plane-strain and tensile work hardening in two sheet steel alloys
, Metall. Trans. A
, A12
, 877
–882
.54.
Wagoner RH and Knibloe JR (1989), The importance of constitutive beha-vior to sheet forming performance, Advance in Constitutive Laws for Eng. Material, Int Acad Publ, 154–158.
55.
Hopperstad
OS
, Berstad
T
, Ilstad
H
, and Lademo
OG
(1998
), Effects of the yield criteria on local deformations in numerical simulation of profile forming
, J. Mater. Process. Technol.
, 80–81
, 551
–555
.56.
Frieman
PA
and Pan
J
(2000
), Effects of plastic anisotropic and yield criteria on prediction of forming limit curves
, Int. J. Mech. Sci.
, 42
(1
), 29
–48
.57.
Yu MH, Yang SY, and Li ZH (2000), Material models in meso-mechanics and macromechanics, Role of Mesomechanics for Development of Science and Technology, GC Sih (ed), Tsinghua Univ Press, Beijing, 239–246.
58.
Chan
KS
(1985
), Effects of plastic anisotropy and yield surface on sheet metal stretchability
, Metall. Trans. A
, 16A
, 629
629
.59.
Kuroda
M
and Tvergaard
V
(2000
), Forming limit diagram for anisotropic metal with different yield criteria
, Int. J. Solids Struct.
, 37
, 5037
–5059
.60.
Boehler JP (ed) (1990), IUTAM/ICM Symp on Yielding, Damage and Failure of Anisotropic Solids, Mech Eng Publ, Edmunds.
61.
Dvorak GJ (ed) (1991), IUTAM Symp on Inelastic Deformation of Composite Materials, Springer-Verlag, New York.
62.
Miller KJ (ed) (1985), Multiaxial Fatigue (papers presented at the 1st Int Conf on Biaxial-Multiaxial Fatigue, 1982), ASME STP, Philadelphia.
63.
Brown MW and Miller KJ (eds) (1989), Biaxial and Multiaxial Fatigue (36 papers presented at 2nd Int Conf on Biaxial-Multiaxial Fatigue), Mech Eng Pub, London, 686 pp.
64.
Kussmaul KF, McDiarmid DL, and Socie DF (eds) (1991), Fatigue under Biaxial and Multiaxial Loading (28 papers presented at 3rd Int Conf on Biaxial-Multiaxial Fatigue, 1989), Mech Eng Pub, London.
65.
Pineau A, Gailletaud G, and Lindley TC (ed) (1996), Multi-axial Fatigue and Design (4th Int Conf on Biaxial-Multiaxial Fatigue, Saint-Germain en Laye, France), Mech Eng Pub, London.
66.
Macha E, Bedkowski W, and Lagoda T (1999), Multiaxial Fatigue and Fracture, Elsevier.
67.
Socie D and Maquis G (1999), Multiaxial Fatigue, ASAE Automotive Engrs.
68.
Krempl
E
and Lu
H
(1984
), The hardening and rate dependent behavior of fully annealed AISI type 304 stainless steel under biaxial in phase and out-of-phase strain cycling at room temperature
, ASME J. Eng. Mater. Technol.
, 106
, 376
376
.69.
Zhang
W
and Akid
R
(1997
), Effect of biaxial mean stress on cyclic stress-train response and behaviour of short fatigue cracks in a high strength spring steel
, Fatigue Fract. Eng. Mater. Struct.
, 20
(2
), 167
–177
.70.
Kim
KS
and Park
JC
(1999
), Shear strain based multiaxial fatigue parameters applied to variable amplitude loading
, Int. J. Fatigue
, 21
(5
), 475
–483
.71.
Findley
WN
(1965
), A theory for the effect of mean stress on fatigue of metals under combined torsion and axial load or bending
, ASME J. Eng. Ind.
, 81
(2
), 301
–306
.72.
Ives
KD
, Kooistra
LF
, and Tacker
JT
(1966
), Equibiaxial low cycle fatigue properties of typical pressure vessel steels
, ASME J. Basic Eng.
, 88
(6
), 745
–754
.73.
Rotvel
F
(1970
), Biaxial fatigue tests with zero mean stress using tubular spasimens
, Int. J. Mech. Sci.
, 12
(5
), 597
–613
.74.
Brown
MW
and Miller
KJ
(1973
), A theory for fatigue failure under multi-axial stress strain condition
, Proc. Inst. Mech. Eng.
, 187
(19
), 745
–755
.75.
Ellyin
F
(1974
), A criterion for fatigue under multiaxial state of Stress
, Mech. Res. Commun.
, 1
(4
), 219
–224
.76.
Miller
KJ
(1977
), Fatigue under complex stress
, Mater. Sci.
, 9
(5
), 432
–438
.77.
Lohr
RD
and Eillison
EG
(1980
), A simple theory for low cycle multiaxial fatigue
, Fatigue Fract. Eng. Mater. Struct.
, 3
(1
), 1
–17
.78.
Lohr
RD
and Eillison
EG
(1980
), Biaxial high strain fatigue testing of 1% Cr-Mo-V steel
, Fatigue Fract. Eng. Mater. Struct.
, 3
(1
), 18
–37
.79.
Garud
YS
(1981
), Multiaxial fatigue-A survey of the state of the art
, J. Test. Eval.
, 9
, 165
–178
.80.
Garud
YS
(1981
), A new approach to the evaluation opf fatigue under multiaxial loading
, ASME J. Eng. Mater. Technol.
, 1981
(2
), 41
–50
.81.
Kandil FA, Miller KJ, and Brown MW (1982), Biaxial low cycle fatigue failure of 316 stainless steel at elevated temperature, Mechanical Behaviour and Nuclear Application of Stainless steel at Elevated Temperature, Metals Society, Book 280, London, 293–209.
82.
Brown MW (1983), Multiaxial fatigue testing and analysis, Fatigue at High Temperature, RP Skelton (ed), Appl Sci Publ, 97–133.
83.
Ellyin
F
, Golos
K
and Xia
Z
(1991
), In phase and out of phase multiaxial fatigue
, ASME J. Eng. Mater. Technol.
, 113
, 112
112
.84.
Sanetra C and Zenner H (1991), Multiaxial fatigue under constant and variable amplitude loading, KF Kussmaul, DL McDiarmid, and DF Socie (ed), Fatigue under Biaxial and Multiaxial Loading, Mech Eng Publ, London.
85.
Chu CC, Conle FA, and Bonnen JJ (1993), Multiaxial stress-strain modeling and fatigue life prediction of SAE axle shafts, Advances in Multiaxial Fatigue, DL Madowel and R Ellis (eds), ASTM STP 1191, Philadelphia, 37–54.
86.
Madowel DL and Ellis R (eds) (1993), Advances in Multiaxial Fatigue, ASTM STP 1191, Philadelphia.
87.
Sonsino
CM
(1995
), Multiaxial fatigue of welded joints under inphase and out-of-phase local strains and stresses
, Int. J. Fatigue
, 17
(1
), 55
–70
.88.
Papadopoulos
IV
(1996
), Invariant formulation of a gradient dependent multiaxial high-cycle fatigue criterion
, Eng. Fract. Mech.
, 55
(4
), 513
–528
.89.
Bocher
L
and Delobelle
P
(1997
), Experimental study of the cyclic behavior of a stainless steen under complex multiaxial loadings in tensiontorsion-internal and external pressure
, Trans SMiRT
, 14
(102/2
), 51
51
.90.
Chen
X
, Gao
Q
, Sun
XF
et al. (1997
), Recent advances of multiaxial low cycle fatigue under nonproportional loading (in Chinese
), Advances in Mechanics
, 27
(3
), 313
–325
.91.
Feng MH, Ma LY, and Lu HX (1998), A new elastic-viscoplastic unified constitutive model for cyclic, creep, monotonic deformation, Strength Theory, Science Press, Beijing, New York, 889–898.
92.
Andrea
C
and Andrea
S
(2001
), Multiaxial high-cycle fatigue criterion for hard metals
, Int. J. Fatigue
, 23
(2
), 135
–145
.93.
Hayhurst
DR
(1972
), Creep rupture under multiaxial states of stress
, J. Mech. Phys. Solids
, 20
, 381
–390
.94.
Leckie
FA
and Hayhurst
DR
(1974
), Creep rupture of structures
, Proc. R. Soc. London, Ser. A
, 340
, 323
323
.95.
Othman
AM
and Hayhurst
DR
(1990
), Multiaxial creep rupture of a model structure using a two parameter material model
, Int. J. Mech. Sci.
, 32
(1
), 35
–48
.96.
Henderson
J
(1979
), An investigation of multi-axial creep characteristics of metals
, ASME J. Eng. Mater. Technol.
, 101
, 356
–364
.97.
Bodner
SR
and Bodner
SR
(ed) (1986
), UTAM Symposium on Damage and Fatigue
, Eng. Fract. Mech.
, 25
, 563
–867
.98.
Fotiu PA, Irschik H, and Ziegler F (1991), Micromechanical foundations of dynamic plasticity with applications to damage structures, Advances in Continuum Mechanics, O Brueller et al. (eds), Springer, Berlin, 338–349.
99.
Ziegler
F
(1992
), Developments in structural dynamic viscoplasticity including ductile damage
, Z. Angew. Math. Mech.
, 72
, T5–T15
T5–T15
.100.
Pineau A and Zaoui A (ed) (1996), IUTAM Symposium on Micromechenics of Plasticity and Damage of Multiphase Materials, Kluwer Acadenic Publ.
101.
Jefferson
AD
(1998
), Plastic damage model for interfaces in cementition materials
, J. Eng. Mech.
, 124
(7
), 775
–782
.102.
Ju JW (ed) (1992), Recent Advances in Damage Mechanics and Plasticity, ASME, AMD-132, MD-30.
103.
Voyiadjis ZG and Kattan PT (1992), Recent Advances in Damage Mechanics and Plasticity JW Ju (ed), ASME, 235–248.
104.
Yazdani
S
(1993
), On a class of continuum damage mechanics theories
, Int. J. Damage Mech.
, 2
, 162
162
.105.
Kawashima K, Nishimura N, and Nakayama O (1998), Ultrasonic evaluation of spall damage accumulation on aluminum and steel plate under repeated impact tests, Strength Theory, Science Press, Beijing, New York, 133–138.
106.
Yang
SY
and Yu
MH
(1998
), A new feasible elasto-plastic damage model in the frame of the theory of mixtures
, Chin J. Geotech. Eng
, 22
(5
), 58
–63
.107.
Yang SY, Yu MH, and Fan SC (1998), A effective multiaxial elasto-plastic damage model for engineering materials, Strength Theory, Science Press, 705–712.
108.
Voyiadjis ZG and Park T (1998), The kinematics of damage for elasto-plastic solids with large strains, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 89–94.
109.
Wang F and Fan SC (1998), Plastic-damage analysis of RC plates, Strength Theory: Applications, Developments and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 693–698.
110.
Yang
SY
and Yu
MH
(2000
), An elasto-plastic damage model for saturated and unsaturated geomaterials (English abstract
), Acta Mech. Sin.
, 32
(2
), 198
–206
.111.
Yang
SY
and Yu
MH
(2000
), Constitutive descriptions of multiphase porous media
, Acta Mech. Sin.
, 32
(1
), 11
–24
(English abstract).112.
Rudnicki
JW
and Rice
JR
(1975
), Conditions for the location of deformation in pressure-sensitive dilatant materials
, J. Mech. Phys. Solids
, 23
, 371
–394
.113.
Rice JR (1976), The localization of plastic deformation, Teoretical and Applied Mechanics (Proc of 14th IUTAM Congress, WT Koiter (ed)), North Holland, Amsterdam, 207–220.
114.
Asaro
RJ
and Rice
JR
(1977
), Strain localization ductile single crystals
, J. Mech. Phys. Solids
, 25
, 309
–338
.115.
Needleman
A
(1979
), Non-normality and bifurcation in plane strain and compression
, J. Mech. Phys. Solids
, 27
, 231
–254
.116.
Bai
YL
(1982
), Thermoplastic instability in simple shear
, J. Mech. Phys. Solids
, 30
, 195
–207
.117.
Peirce
D
, Asaro
RJ
and Needleman
A
(1983
), Materials dependence and localized deformation in crystalline solids
, Acta Metall.
, 31
, 1951
–1976
.118.
Frantziskonis
G
and NAME
CS
(1987
), Analysis of a strain-softening constitutive model
, Int. J. Solids Struct.
, 23
(6
), 751
–767
.119.
Bazant
ZP
and Pijaudier-Cabot
G
(1988
), Nonlocal continuum damage, localization instability and convergence
, ASME J. Appl. Mech.
, 55
, 287
–293
.120.
de Borst
R
(1988
), Bifurcation in finite element methods with a non-associated flow law
, Int. J. Numer. Analyt. Meth. Geomech.
, 12
, 99
–166
.121.
Li GC and Jaener M (1993), Meso-Structural Mechanics at Plastic Large Strain, Science Press, Beijing.
122.
Bardet JP and Proubet J (1991), A shear band analysis in elastoplastic granular material, Anisotropy and Localization of Plastic Deformation, J-P Boehler and AS Khan (eds), Elsevier, London, New York, 35–38.
123.
Li
GC
(1990
), Numerical analysis of shear-band bifurcation
, Acta Mech. Sin.
, (English Ed.), 6
, 22
–28
.124.
Chen WF and Yamaguchi E (1990), (PAPER TITLE) Micromechanics of Failure of Quasi-Brittle Materials, SP Shah, SE Swartz, and ML Wang (eds), Elsevier, London 265–274.
125.
Dietsche A, Steinmann P, and Willam K (1991), Micropolar elasto-plasticity and its role in localization analysis, Anisotropy and Localization of Plastic Deformation, J-P Boehler and AS Khan (eds), Elsevier, London, New York, 35–38.
126.
Ottosen
NS
and Runesson
K
(1991
), Properties of discontinuous bifurcation solutions in elasto-plasticity
, Int. J. Solids Struct.
, 27
, 401
–421
.127.
Tvergaad V and van der Giessen E (1991), Effect of triaxial tension on flow localization for different plastic spin, Anisotropy and Localization of Plastic Deformation, J-P Boehler and AS Khan (ed), Elsevier Appl Sci London, 1–94.
128.
Nemat-Nasser S and Hori M (1993), Micromechanics: Overall Properties of Heterogeneous Materials, Elsevier, Northholland.
129.
Yang W and Lee WB (1993), Mesoplasticity and its Application, Springer-Verlag, Berlin.
130.
Yu MH and Zeng WB (1993), Mesomechanical simulation of failure criterion for a composite material, Macro-Meso-Micro Mechanical Properties of Materials, M Tokuda and BY Xu (ed), Mie Academic Press, 571–576.
131.
Needleman
A
(1994
), Computation modeling of materials failure
, Appl. Mech. Rev.
, 47
(6
, Pt2), 34
–42
.132.
Aifantis
EC
(1994
), Gradient effects at macro, micro and nano scales
, J. Mech. Behav. Mater.
, 5
, 355
–375
.133.
Batra RC and Zbib HM (1994), Materials Instabilities, ADM-183, ASME, New York.
134.
Chambon R, Desrues L, and Vardoulakis J (eds) (1994), Localisation and Bifurcation Theory for Soil and Rock, Balkema.
135.
Wu W and Vardoulakis I (1994), (PAPER TITLE?) Localisation and Bifurcation Theory for Soils and Rocks, R Chambon, J Desrues, and I Vardoulakis (eds), Balkema, Rotterdam, 237–247.
136.
Desai CS and Gallagher RH (eds) (1984), Mechanics of Engineering Materials, John Wiley & Sons Ltd.
137.
Ghoniem N (ed) (1995), Plastic and Fracture Instabilities in Materials, AMD-Vol 200/MD-57, ASME, New York.
138.
Tomita
Y
(1994
), Simulations of plastic instabilities in solid mechanics
, Appl. Mech. Rev.
, 47
(6
, Pt1), 171
–205
.139.
Zbib
HM
, Shawki
TG
, and Batra
RC
(1992
), Materials instabilities
, Appl. Mech. Rev.
, 45
(3
, Pt2), S1–S173
S1–S173
.140.
Libersky LD and Petschek AG (1992), Smoothed particle hydrodynamics with strength of materials, The Next Free Lagrange Conference, HE Trease, JW Fritts, and WP Crowley (eds), Springer, Jackson Hole WY.
141.
Oger
L
and Savage
SB
(1999
), Smoothed particle hydrodynamics for cohecive grains
, Comput. Methods Appl. Mech. Eng.
, 180
, 169
–183
.142.
Fleck
NA
and Hutchinson
JW
(1997
), Strain gradient plasticity
, Adv. Appl. Mech.
, 33
, 295
–261
.143.
Suquet P (ed) (1997), Continuum Micromechanics, Springer, Wien.
144.
Shah SP, Swartz SE, and Wang ML (eds) (1990), Micromechanics of Failure of Quasi-Brittle Materials, Elsevier, London, 265–274.
145.
Kuksenko VS and Tamuzs VP (eds) (1981), Fracture Micromechanics of Polymer Materials, Martinus Nijhoff Publ, Boston.
146.
Perzyna
P
(1963
), The constitutive equation for rate sensitive plastic material
, Q. Appl. Math.
, 20
(4
), 321
–332
.147.
Zukas JA, Nicholas T, Swift HF et al. (1982), Impact Dynamics, Wiley, New York.
148.
Ma GW, Hao H, Iwasaki S, Miyamoto Y, and Deto H (1998), Plastic behavior of circular plate under soft impact, Strength Theory, Science Press, Beijing, New York, 957–963.
149.
Ziegler
F
(1992
), Nonlinear structural response to impact and vibrational loading
, Eur. J. Mech. A/Solids
, 11
, 99
–114
.150.
Irschik
H
and Ziegler
F
(1995
), Dynamic processes in structural thermo-visco-plasticity
, Appl. Mech. Rev.
, 48
(6
), 301
–316
.151.
Gao CY, Shi HJ, Yao ZH, Hua WX, and Bai CH (1998), Dynamic fracture criteria of thin cylindrical shell subject to explosive loading at high strain rate, Strength Theory, Science Press, Beijing, New York, 945–950.
152.
Xu YH, Chen YM et al. (1998), The effect of stress characteristics on impact wear mechanism, Strength Theory, Science Press, 483–490.
153.
Wang
ZP
and Jiang
Q
(1997
), A yield criterion for porous ductile media at high strain rate
, ASME J. Appl. Mech.
, 64
, 503
–509
.154.
Gallagher
RH
, Padlog
J
, and Bijlaard
PP
(1962
), Stress analysis of heated complex shapes
, J. Am. Rocket. Soc.
, 32
, 700
–707
.155.
Argyris
JH
(1965
), Elasto-plastic matric displacement analysis of three-D continuua
, J. R. Aeronaut. Soc.
, 69
, 633
–636
.156.
Pope GG (1965), A discrete element method for analysis of plane elasto-plastic strain problems, 1st Conf Math Meth in Struct Mech, 65–028, Farnborough.
157.
Theokaris
PS
and Marketos
E
(1964
), Elastic-plastic analysis of perforated thin strips of strain-hardening material
, J. Mech. Phys. Solids
, 12
, 377
–390
.158.
Reyes SF and Deere DU (1966), Elasto-plastic analysis of underground openings by the finite element method, Proc. 1st ICRM. 11, 477–486, Lisbon.
159.
Marcal
PV
and King
IP
(1967
), Elastic-plastic analysis of 2-D stress system by FEM
, Int. J. Mech. Sci.
, 9
, 143
–155
.160.
Yamada
Y
, Yoshimura
N
, and Sakurai
T
(1968
), Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the FEM
, Int. J. Mech. Sci.
, 10
, 343
–354
.161.
Zienkiewicz
OC
, Valliappan
S
, and King
IP
(1969
), Elasto-plastic solutions of engineering problems. Initial-stress, finite element approach
, Int. J. Numer. Methods Eng.
, 1
, 75
–100
.162.
Richards
RM
and Blacklock
JR
(1969
), Finite element analysis of inelastic structures
, AIAA J.
, 7
(3
), 432
–438
.163.
Pifko
A
and Isakson
G
(1969
), A finite element method for the plastic buckling analysis of plates
, AIAA J.
, 7
(10
), 1950
–1957
.164.
Oden JT (1972), Finite Element of Nonlinear Continua, McGraw-Hill, New York.
165.
Nayak
GC
and Zienkiewicz
CC
(1972
), Convenient form of stress invariants for plasticity
, J. Struct. Div. ASCE
, 4
, 949
–953
.166.
Valliappan
S
and Doolan
TF
(1972
), Nonlinear stress analysis of reinforced concrete
. J. Struct. Div. ASCE
, 98
(4
), 885
–898
.167.
Argyris
JH
, Faust
G
, Szimmat
J
, Warnke
EP
, and Willam
KJ
(1974
), Recent developments in the finite element analysis of prestressed concrete reactor vessels
, Nucl. Eng. Des.
, 28
, 42
–75
.168.
Gudehus G (ed) (1977), Finite Elements in Geomechanics, John Wiley & Sons Ltd.
169.
Owen DRJ and Hinton E (1980), Finite Elements in Plasticity: Theory and Practice, Pineridge Press, Swansea.
170.
Telles TCF and Brebbia CA (1981), Elasto-plastic boundary element analysis, Non-linear Finite Element Analysis in Structural Mechanics, W Wunderlich, E Stein, and KJ Bathe, (eds), Springer-Verlag.
171.
Afzali M and Devalan P (1985), CASTOR-A package of computer programs for FEM analysis of engineering problems, Finite Element Systems (A Handbook), CA Brebbia (ed), Springer-Verlag, Berlin, 187–222.
172.
Bathe KJ and Larsson G (1985), The use of ADINA in engineering practice, Finite Element Systems (A Handbook), CA Brebbia (ed), Springer-Verlag, Berlin, 59–78.
173.
de Borst R (1985), ADIAN-A comprehensive, but flexible finite element system, Finite Element Systems (A Handbook), CA Brebbia (ed), Springer-Verlag, Berlin, 299–312.
174.
Bougrelle P (1985), TITUS: A general finite element system, Finite Element Systems (A Handbook), CA Brebbia, (ed), Springer-Verlag, Berlin, 733–754.
175.
Brebbia CA, Danson D, and Baynham J (1985), BEASY boundary element analysis system, Finite Element Systems (A Handbook), CA Brebbia (ed), Springer-Verlag, Berlin, 141–158.
176.
Kransz AS (ed), (1990) Constitutive Laws of Plastic Deformations and Fractures, Klunwer Academic, Dordrecht.
177.
Faruque
MO
and Desai
CS
(1985
), Implementation of a general constitutive model for geological materials
, Int. J. Num. Ana. Methods in Geomech
9
(5
), 415
–436
.178.
Ferguson GH et al. (1985), DIAL-Finite element analysis system, Finite Element Systems, CA Brebbia, (ed), Springer-Verlag, Berlin, 279–298.
179.
Goos R (1985), The ASKA finite element system. In: Finite Element Systems (A Handbook), CA Brebbia, (ed), Springer-Verlag, Berlin, 115–140.
180.
Hibbitt HD (1985) ABQUS-A general purpose liniar and nonlinear finite element codes, Finite Element Systems (A Handbook), CA Brebbia (ed), Springer-Verlag, Berlin, 21–58.
181.
Horne S (1985), MSC/NASTRAN, Finite Element Systems (A Handbook), CA Brebbia (ed), Springer-Verlag, Berlin, 557–564.
182.
Hulst E (1985), An overview of the MARC general purpose finite element program, Finite Element Systems (A Handbook), CA Brebbia (ed), Springer-Verlag, Berlin, 473–482.
183.
Kohnke PC (1985), ANSYS, Finite Element Systems (A Handbook), CA Brebbia (ed), Springer-Verlag, Berlin, 79–86.
184.
Lashkari M et al. (1985), COSMOS7 A structural analysis finite element program, Finite Element Systems (A Handbook), CA Brebbia (ed), Springer-Verlag, Berlin, 245–258.
185.
Sloan
SW
and Booker
JR
(1986
), Removal of singularities in Tresca and Mohr-Coulomb yield function
, Commun. Appl. Numer. Methods
, 2
, 173
–179
.186.
Marques
JM
(1984
), Stress computation in elastoplasticity
, Eng. Comput.
, 1
, 42
–51
.187.
Yin
YQ
(1984
), Loading criteria for a singular yield surface (in Chinese
), Acta Mechanica Solida Sinica
, 6
(2
), 282
–285
.188.
Oritiz
M
and Popov
EP
(1985
), Accuracy and stability of integration algorithms for elastoplastic constitutive relations
, Int. J. Numer. Methods Eng.
, 21
, 1561
–1576
.189.
Yin
YQ
and Zhou
Z
(1985
), Constitutive relation in the singular point of yield criterion for geomaterials
, Chin. J. Rock Mech. Eng.
, 4
(1
), 33
–38
.190.
de Borst
R
(1987
), Integration of plasticity equations for singular yield functions
, Comput. Struct.
, 26
, 823
–829
.191.
Ortiz
M
, Leroy
Y
and Needleman
A
(1987
), A finite element method for localized failure analysis
, Comput. Methods Appl. Mech. Eng.
, 61
, 89
–124
.192.
Runesson
K
, Sture
S
, and Willam
K
(1988
), Integration in computational plasticity
, Comput. Struct.
, 30
(1-2
), 119
–130
.193.
Pankaj and Bicanic N (1989), On multivector stress returns in Mohr-Coulomb plasticity, Computational Plasticity: Models, software, and Applications, DRJ Owen, E Hinton, and E Onate (eds), Pineridge Press.
194.
Owen DRJ, Hinton E, and Onate E (1989), Computational Plasticity: Models, Software and Applications, Pineridge Press (101 papers, 1460 pp).
195.
de Borst R (1989), Computational strategies for strongly curved and non-smooth yield criteria with applications to localisation of deformation. In: Computational Plasticity: Models, Software & Applications, DRJ Owen, E Hinton, and E Onate (eds), Pineridge Press, 237–261.
196.
Burd HJ, Yu HS, and Houlsby GT (1989), Finite element implementation of frictional plasticity models with dilation, Advance in Constitutive Laws for Eng Material, Int Acad Publ, 783–788.
197.
Smith DL (ed) (1990), Mathematical Programming Methods in Structural Plasticity, (21 papers, 435 pp), Springer-Verlag, Wien.
198.
Chen WF and Zhang H (1991), Structural Plasticity: Theory, Problems and CAE Software, Springer-Verlag, 125–168.
199.
Yu MH and Li YM (1991), Twin shear constitutive theory and its computational implementation, Computational Mechanics, YK Cheung et al. (eds), Balkema, Rotterdam, 875–879.
200.
Strin E (1993), Progress in Computational Analysis of Inelastic Structures (CISM No 321), Springer-Verlag,
201.
Doltsinis IS (ed) (1989), Advances in Computational Nonlinear Mechanics (CISM), Springer-Verlag, Wien.
202.
Desai CS and Siriwardane HJ (1984), Constitutive Laws for Engineering Materials, Printice-Hall, Englewood Cliffs, NJ.
203.
Desai CS (1990), Modelling and testing: Implementation of numerical models and their application in practice, Numerical Methods and Constitutive Modelling in Geomech., CS Desai and G Gioda (eds), Springer, Wien.
204.
Kobayashi AS et al. (1989), Metal Forming and the Finite Element Method. Oxford Univ Press, New York.
205.
Calloch S and Marquis D (1996), Triaxial tension-compression loadings in cyclic clasto-plasticity: experimental and numerical aspects, Proc. AEPA, 135.
206.
Larsson
R
and Runesson
K
(1996
), Implicil integration and consistent linearization for yield criteria of the Mohr-Coulomb type
, Mech. Cohesive-Frict. Mater.
, 1
, 367
–383
.207.
Jeremic
B
and Sture
S
(1997
), Implicit integration in elasto-plastic geotechnics
, Mech. Cohesive-Frict. Mater.
, 2
, 165
–183
.208.
Peric
D
and de Souza Neto
EA
(1999
), A new computational model for the Tresca plasticity at finite strains with an optimal parametrization in the principal space
, Comput. Methods Appl. Mech. Eng.
, 171
(3–4
), 463
–489
.209.
Granlund
J
and Olsson
A
(1998
), Modelling of the plastic behaviour of structural steel based on biaxial testing
, J. Construct Steel Res
, 46
(1–3
), 404
–405
.210.
Tun ZL, Hasegawa T, and Thai NC (1998), Numerical simulation of flow deformation behaviour of two and three phase porous media, Strength Theory, Science Press, Beijing, New York, 615–620.
211.
Zienkiewicz
OC
, Owen
DRJ
, Phyillips
DV
, and Nayak
GC
(1970
), Finit element method in analysis of reactor vessels
, Nucl. Eng. Des.
, 20
, 507
–541
.212.
Nilson
AH
(1968
), Nonlinear analysis of reinforced concrete by the finite element method
, ACI
, 65
(9
), 757
–766
.213.
FLAC-3D (1997), Fast Lagrangian Analysis of Continua in 3-Dimensions, Version 2.0, User’s Manual, Itasca Consuliting Group, Inc (US).
214.
Kou
XD
, Zhou
WY
, and Yang
RQ
(2001
), The stability analysis on the high slopes of Three-Gorges shiplock using FLAC-3D
, Chin J. Rock Mech Eng
, 20
(1
), 6
–10
.215.
Yin YJ, Tsuta T, and Iwamoto T (1998), Theoretical and experimental studies on micro void evolution process using rigid plastic FEM model based on Gurson type yield function, Strength Theory. Science Press, Beijing, New York, 633–638.
216.
Hult J (ed) (1972), 2nd IUTAM Symp on Creep in Structures, Springer-Verlag, Berlin.
217.
Lippmaun H (ed) (1979), IUTAM Symp on Metal Forming Plasticity, Springer-Verlag, Berlin.
218.
Nemat-Nasser S (ed) (1981), IUTAM Symp on Three-Dimensional Constitutive Relations and Ductile Fracture, Norcth-Hollant Publ, Amsterdam.
219.
Ponter ARS and Hayhurst DR (eds) (1981), 3rd IIUTAM Symp on Creep in Structures, Springer-Verlag, Berlin.
220.
Vermeer PA and Luger HJ (ed) (1982), IUTAM Symp on Deformation and Failure of Granular Materials, Balkema, Rotterdam.
221.
Bazant ZP (ed) (1985), IUTAM Symp on Mechanics of Geomaterials: Rocks, Concretes, Soils, John Wiley, London.
222.
Zyczkowski M (ed) (1992), IUTAM Symp on Creep in Structures, Springer-Verlag, Berlin.
223.
Ortiz
M
and Shih
C F
(eds) (1994
), IUTAM Symp on Computational Mechanics and Materials
, J. Model Simul Mat Sci. Eng
, 2
(3A
), 421
–782
.224.
Carpinteri A (ed) (1995), IUTAM Symp on Size-Scale Effects in the Failure Mechanisms of Materials and Structures, E & FN SPON, London.
225.
Fleck NA and Cocks ACF (eds) (1997), IUTAM Symp on Mechanics of Granular and Porous Materials, Kluwer Academic Publ, Dordrecht.
226.
Bruhns OT and Stein E (eds) (1997), IUTAM Symp on Micro-and Macrostructural Aspects of Thermoplasticity, Kluwer Academic Publ.
227.
Fulachier L, Lumley JL, and Anselmet F (1998) (eds), IUTAM Symp on Mechanics of Granular and Porous Materials, Kluwer Academic Publ, Dordrecht.
228.
Ehlers W (ed) (1999), IUTAM Symp on Theoretical and Numerical Methods in Continuum Mechanics of Porous Materials, Kluwer Acad Publ.
229.
Oden JT et al. (eds) (1974), Proc of Int Conf On Comp Methods in Nonlinear Mech Univ of Texas, Austin, TX.
230.
Desai CS and Christian JT (1977), Numerical Methods in Geotechnical Engineering, (PUBLISHER?).
231.
Saada AS and Bianchini GH (1988), Constitutive Equations for Granular Non-Cohesive Soils, Balkema, Rotterdam.
232.
William KJ (ed) (1984), Constitutive Equations Macro and Computational Aspects, NY United Engineering Center, 272 pp.
233.
Axelrad DR and Muschik W (ed) (1988), Constitutive Laws and in Microstructures Proc, Springer, Berlin.
234.
Rajendran AM and Batra RC (1995), Constitutive Laws: Theory, Experiments, and Numerical Implementation, CIMNE, Barcelona.
235.
Chandra J and Srivastav RP (eds) (1987), Constitutive Models of Deformation, SIAM, Philadelphia.
236.
Kolymbas D (ed) (2000), Constitutive Modelling of Granular Materials, Springer, Berlin.
237.
Dungar R, Pande GN, and Studer JA (eds) (1982), Numerical Models in Geomechanics (NUMOG, Zurich), Balkema, Rotterdam.
238.
Pande GN and Pietruszczak S (eds) (1992), Numerical Models in Geomechanics (NUMOG-IV, Swansea), Balkema, Rotterdam.
239.
Pande GN and Pietruszczak S (eds) (1995), Numerical Models in Geomechanics (NUMOG-V, Davos), Balkema, Rotterdam.
240.
Pietruszczak S and Pande GN (eds) (1989), Numerical Models in Geomechanics (NUMOG III), Elsevier, London.
241.
Pietruszczak S and Pande GN (eds) (1997), Numerical Models in Geomechanics (NUMOG-VI, Davos), Balkema, Rotterdam.
242.
Boehler JP and Khan AS (eds) (1991), Anisotropy and Localization of Plastic Deformation, Elsevier, London, New York.
243.
Boehler JP (ed) (1993), Failure Criteria of Structured Media, Balkema, Rotterdam.
244.
Yu MH and Fan SC (eds) (1998), Strength Theory: Applications, Developments and Prospect for 21st Century, Science Press, Beijing, New York, 1178 pp.
245.
Ansari F (1998), Fiber optic sensor for testing of high strength concrete triaxial compression, Strength Theory: Applications, Developments, and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 1–6.
246.
Gong YN, Qian C, and Li JC (1998), Failure criteria of materials in impact problems of aero-structures future, Strength Theory: Applications, Developments, and Propsects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 49–54.
247.
Sih GC (1998), Reconcilation of surface and volume energy density in continuum mechanics, Strength Theory: Applications, Developments, and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 69–78.
248.
Yu MH (1998), Fifty years of research on the strength theory in China, Strength Theory, Science Press, Beijing, New York, 95–114.
249.
Mean
ME
and Hutchinson
JW
(1985
), Influence of yield surface curvation on flow localization in dilatant plasticity
, Mech. Mater.
, 4
, 395
–407
.250.
Vardoulakis
I
and Graff
B
(1985
), Calibration of constitutive models for granular materials using data from biaxial experiments
, Geotechnique
, 35
, 299
–317
.251.
Wegener
K
and Schlegel
M
(1996
), Suitability of yield functions for the approximation of subsequent yield surfaces
, Int. J. Plast.
, 12
(9
), 1151
–1177
.252.
Moin K and Pankaj (1998), Post-peak behavior simulation using different failure theories, Strength Theory, Science Press, Beijing, New York, 1121–1126.
253.
Duan M, Miyamoto Y, Iwasaki S, Deto H, and Zhou BC (1998), Estimation of buckling loads for cylindrical roof shell structures based on different strength theory, Strength Theory, Sience Press, Beijing, New York, 1021–1026.
254.
Zyczkowskii
M
(1999
), Discontinuous bifurcations in the case of the Burzynski-Torre yield criterion
, Appl. Mater. Res.
, 132
(1–4
), 19
–30
.255.
Wang F and Fan SC (1998), Limit pressures of thick-walled tubes using different yield criteria, Strength Theory: Applications, Developments, and Prospects for 21st Century, MH Yu and SC Fan (eds), Science Press, Beijing, New York, 1047–1052.
256.
Zhang
YQ
and Yu
MH
(2001
), Discontinuous bifurcations of metallic materials for plane stress
, Chin. J. Mech. Eng.
, 37
(4
), 87
–91
.257.
Dvorak GJ (ed) (1999), Research Trends in Solid Mechanics, Pergamon, New York.
258.
Sih GC (2000), Micromechanics associated with thermal/mechanical interaction for polycrystals, Role of Mesomechanics for Development of Science and Technology, Tsinghua Univ Press, Beijing, 3–20.
259.
Iino M and Kaminishi K (1998), Influence of crack-end atomic attractions on stress distributions around crack tips, Strength Theory, Science Press, Beijing, New York, 793–798.
Copyright © 2002
by ASME
You do not currently have access to this content.
