We investigate the properties of high-amplitude stress waves propagating through chains of elastic–plastic particles using experiments and simulations. We model the system after impact using discrete element method (DEM) with strain-rate dependent contact interactions. Experiments are performed on a Hopkinson bar coupled with a laser vibrometer. The bar excites chains of 50 identical particles and dimer chains of two alternating materials. After investigating how the speed of the initial stress wave varies with particle properties and loading amplitude, we provide an upper bound for the leading pulse velocity that can be used to design materials with tailored wave propagation.
Issue Section:
Research Papers
References
1.
Nesterenko
, V.
, 2001
, Dynamics of Heterogeneous Materials
, Springer
, New York
.2.
Job
, S.
, Melo
, F.
, Sokolow
, A.
, and Sen
, S.
, 2007
, “Solitary Wave Trains in Granular Chains: Experiments, Theory, and Simulations
,” Granular Matter
, 10
(1), pp. 13
–20
.10.1007/s10035-007-0054-23.
Daraio
, C.
, Nesterenko
, V. F.
, Herbold
, E. B.
, and Jin
, S.
, 2006
, “Tunability of Solitary Wave Properties in One-Dimensional Strongly Nonlinear Phononic Crystals
,” Phys. Rev. E
, 73
(2
), p. 026610
.10.1103/PhysRevE.73.0266104.
Doney
, R. L.
, Agui
, J. H.
, and Sen
, S.
, 2009
, “Energy Partitioning and Impulse Dispersion in the Decorated, Tapered, Strongly Nonlinear Granular Alignment: A System With Many Potential Applications
,” J. Appl. Phys.
, 106
(6), p. 064905
.10.1063/1.31904855.
Nesterenko
, V. F.
, Daraio
, C.
, Herbold
, E. B.
, and Jin
, S.
, 2005
, “Anomalous Wave Reflection at the Interface of Two Strongly Nonlinear Granular Media
,” Phys. Rev. Lett.
, 95
(15
), p. 158702
.10.1103/PhysRevLett.95.1587026.
Daraio
, C.
, Nesterenko
, V. F.
, Herbold
, E. B.
, and Jin
, S.
, 2006
, “Energy Trapping and Shock Disintegration in a Composite Granular Medium
,” Phys. Rev. Lett.
, 96
(5
), p. 058002
.10.1103/PhysRevLett.96.0580027.
Fraternali
, F.
, Porter
, M. A.
, and Daraio
, C.
, 2008
, “Optimal Design of Composite Granular Protectors
,” Mech. Adv. Mater. Struct.
, 17
(1
), pp. 1
–19
.10.1080/153764908027107798.
Hong
, J.
, 2005
, “Universal Power-Law Decay of Impulse Energy Granular Protectors
,” Phys. Rev. Lett.
, 94
(10
), p. 108001
.10.1103/PhysRevLett.94.1080019.
Ngo
, D.
, Fraternali
, F.
, and Daraio
, C.
, 2012
, “Highly Nonlinear Solitary Wave Propagation in Y-Shaped Granular Crystals With Variable Branch Angles
,” Phys. Rev. E
, 85
(3
), p. 036602
.10.1103/PhysRevE.85.03660210.
Leonard
, A.
, Ponson
, L.
, and Daraio
, C.
, 2014
, “Wave Mitigation in Ordered Networks of Granular Chains
,” J. Mech. Phys. Solids
, 73
, pp. 103
–117
.10.1016/j.jmps.2014.08.00411.
Jayaprakash
, K. R.
, Starosvetsky
, Y.
, and Vakakis
, A. F.
, 2011
, “New Family of Solitary Waves in Granular Dimer Chains With No Precompression
,” Phys. Rev. E
, 83
(3
), p. 036606
.10.1103/PhysRevE.83.03660612.
Molinari
, A.
, and Daraio
, C.
, 2009
, “Stationary Shocks in Periodic Highly Nonlinear Granular Chains
,” Phys. Rev. E
, 80
(5
), p. 056602
.10.1103/PhysRevE.80.05660213.
Porter
, M. A.
, Daraio
, C.
, Herbold
, E. B.
, Szelengowicz
, I.
, and Kevrekidis
, P. G.
, 2008
, “Highly Nonlinear Solitary Waves in Periodic Dimer Granular Chains
,” Phys. Rev. E
, 77
(1
), p. 015601
.10.1103/PhysRevE.77.01560114.
Bragança
, E. A.
, Rosas
, A.
, and Lindenberg
, K.
, 2013
, “Binary Collision Approximation for Multi-Decorated Granular Chains
,” Physica A
, 392
(24
), pp. 6198
–6205
.10.1016/j.physa.2013.07.07615.
Sen
, S.
, Hong
, J.
, Bang
, J.
, Avalos
, E.
, and Doney
, R.
, 2008
, “Solitary Waves in the Granular Chain
,” Phys. Reports
, 462
(2
), pp. 21
–66
.10.1016/j.physrep.2007.10.00716.
Boechler
, N.
, Yang
, J.
, Theocharis
, G.
, Kevrekidis
, P. G.
, and Daraio
, C.
, 2011
, “Tunable Vibrational Band Gaps in One-Dimensional Diatomic Granular Crystals With Three-Particle Unit Cells
,” J. App. Phys.
, 109
(7), p. 074906
.10.1063/1.355645517.
Hoogeboom
, C.
, Man
, Y.
, Boechler
, N.
, Theocharis
, G.
, Kevrekidis
, P. G.
, Kevrekidis
, I. G.
, and Daraio
, C.
, 2013
, “Hysteresis Loops and Multi-Stability: From Periodic Orbits to Chaotic Dynamics (and Back) in Diatomic Granular Crystals
,” Europhys. Lett.
, 101
(4
), p. 44003
.10.1209/0295-5075/101/4400318.
Herbold
, E. B.
, Kim
, J.
, Nesterenko
, V. F.
, Wang
, S.
, and Daraio
, C.
, 2009
, “Pulse Propagation in a Linear and Nonlinear Diatomic Periodic Chain: Effects of Acoustic Frequency Band-Gap
,” Acta Mech.
, 205
(1–4
), pp. 85
–103
.10.1007/s00707-009-0163-619.
Breindel
, A.
, Sun
, D.
, and Sen
, S.
, 2011
, “Impulse Absorption Using Small, Hard Panels of Embedded Cylinders With Granular Alignments
,” App. Phys. Lett.
, 99
(6
), p. 063510
.10.1063/1.362446620.
Tournat
, V.
, Gusev
, V. E.
, and Castagnede
, B.
, 2004
, “Self-Demodulation of Elastic Waves in a One-Dimensional Granular Chain
,” Phys. Rev. E
, 70
(5
), p. 056603
.10.1103/PhysRevE.70.05660321.
Ganesh
, R.
, and Gonella
, S.
, 2014
, “Invariants of Nonlinearity in the Phononic Characteristics of Granular Chains
,” Phys. Rev. E
, 90
(2
), p. 023205
.10.1103/PhysRevE.90.02320522.
Cabaret
, J.
, Tournat
, V.
, and Bequin
, P.
, 2012
, “Amplitude-Dependent Phononic Processes in a Diatomic Granular Chain in the Weakly Nonlinear Regime
,” Phys. Rev. E
, 86
(4
), p. 041305
.10.1103/PhysRevE.86.04130523.
Coste
, C.
, and Gilles
, B.
, 1998
, “On the Validity of Hertz Contact Law for Granular Material Acoustics
,” Eur. Phys. J. B
, 7
(1
), pp. 155
–168
.10.1007/s10051005059824.
Pal
, R. K.
, Awasthi
, A. P.
, and Geubelle
, P. H.
, 2013
, “Wave Propagation in Elasto-Plastic Granular Systems
,” Granular Matter
, 15
(6
), pp. 747
–758
.10.1007/s10035-013-0449-125.
Pal
, R. K.
, Awasthi
, A. P.
, and Geubelle
, P. H.
, 2014
, “Characterization of Wave Propagation in Elastic and Elastoplastic Granular Chains
,” Phys. Rev. E
, 89
(1
), p. 012204
.10.1103/PhysRevE.89.01220426.
Wang
, E.
, Manjunath
, M.
, Awasthi
, A. P.
, Pal
, R. K.
, Geubelle
, P. H.
, and Lambros
, J.
, 2014
, “High-Amplitude Elastic Solitary Wave Propagation in 1-D Granular Chains With Preconditioned Beads: Experiments and Theoretical Analysis
,” J. Mech. Phys. Solids
, 72
, pp. 161
–173
.10.1016/j.jmps.2014.08.00227.
Shoaib
, M.
, and Kari
, L.
, 2011
, “Discrete Element Simulations of Elastoplastic Shock Wave Propagation in Spherical Particles
,” Adv. Acoust. Vib.
, 2011
, pp. 1
–9
.10.1155/2011/12369528.
Thornton
, C
., 1995
, “Coefficient of Restitution for Collinear Collisions of Elastic-Perfectly Plastic Spheres
,” ASME J. Appl. Mech.
, 62
(2
), pp. 383
–386
.10.1115/1.278731929.
Vu-Quoc
, L.
, Zhang
, X.
, and Lesburg
, L.
, 1999
, “A Normal Force–Displacement Model for Contacting Spheres Accounting for Plastic Deformation: Force-Driven Formulation
,” ASME J. Appl. Mech.
, 67
(2
), pp. 363
–371
.10.1115/1.130533430.
Wang
, E.
, On
, T.
, and Lambros
, J.
, 2013
, “An Experimental Study of the Dynamic Elasto-Plastic Contact Behavior of Dimer Metallic Granules
,” Exp. Mech.
, 53
(5
), pp. 883
–892
.10.1007/s11340-012-9696-z31.
Burgoyne
, H. A.
, and Daraio
, C.
, 2014
, “Strain-Rate-Dependent Model for the Dynamic Compression of Elastoplastic Spheres
,” Phys. Rev. E
, 89
(3
), p. 032203
.10.1103/PhysRevE.89.03220332.
On
, T.
, LaVigne
, P. A.
, and Lambros
, J.
, 2014
, “Development of Plastic Nonlinear Waves in One-Dimensional Ductile Granular Chains Under Impact Loading
,” Mech. Mater.
, 68
, pp. 29
–37
.10.1016/j.mechmat.2013.06.01333.
Pal
, R. K.
, Morton
, J.
, Wang
, E.
, Lambros
, J.
, and Geubelle
, P. H.
, 2015
, “Impact Response of Elasto-Plastic Granular Chains Containing an Intruder Particle
,” ASME J. Appl. Mech.
, 82
(1
), p. 011002
.10.1115/1.402895934.
On
, T.
, Wang
, E.
, and Lambros
, J.
, “Plastic Waves in One-Dimensional Heterogeneous Granular Chains Under Impact Loading: Single Intruders and Dimer Chains
,” Int. J. Solids Struct.,
61
, pp. 81
–90
.10.1016/j.ijsolstr.2015.02.00635.
Wang
, E.
, Geubelle
, P.
, and Lambros
, J.
, 2013
, “An Experimental Study of the Dynamic Elasto-Plastic Contact Behavior of Metallic Granules
,” ASME J. Appl. Mech.
, 80
(2
), p. 021009
.10.1115/1.400725436.
Gray
, G. T.
, 2000
, “Classic Split-Hopkinson Pressure Bar Testing
,” ASM Handbook: Mechanical Testing and Evaluation
, Vol. 8
, ASM International
, Novelty, OH
.37.
Stratasys
, 2014
, “PolyJet Materials Data Sheet
,” Stratasys, Eden Prarie, MN, http://www.stratasys.com/∼/media/main/secure/material%20specs%20ms/polyjet-material-specs/polyjet_materials_data_sheet.pdf38.
Daraio
, C.
, Nesterenko
, V. F.
, Herbold
, E. B.
, and Jin
, S.
, 2005
, “Strongly Nonlinear Waves in a Chain of Teflon Beads
,” Phys. Rev. E
, 72
(1
), p. 016603
.10.1103/PhysRevE.72.01660339.
Ashcroft
, N. W.
, and Mermin
, N. D.
, 1976
, Solid State Physics
, Saunders College Publishing
, Orlando, FL
.40.
Hascoet
, E.
, Herrmann
, H. J.
, and Loreto
, V.
, 1999
, “Shock Propagation in a Granular Chain
,” Phys. Rev. E
, 59
(3
), pp. 3202
–3206
.10.1103/PhysRevE.59.320241.
Tasi
, J.
, 1980
, “Evolution of Shocks in a One Dimensional Lattice
,” J. Appl. Phys.
, 51
(11
), pp. 5804
–5815
.10.1063/1.32753842.
Zhuang
, S.
, Ravichandran
, G.
, and Grady
, D. E.
, 2003
, “An Experimental Investigation of Shock Wave Propagation in Periodically Layered Composites
,” J. Mech. Phys. Solids
, 52
(2
), pp. 245
–265
.10.1016/S0022-5096(02)00100-XCopyright © 2015 by ASME
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