The Ogden strain energy expression is expanded to an optimal number of terms characterizing materials to predict any response of any mode of deformation well. The effect of each term generating the model is highlighted in the corresponding state of deformation, i.e., influence domain: Moderate stretch, transition, or stiffening region, with the help of the proposed method.

1.
Rivlin
,
R. S.
, 1956,
Rheology: Theory and Applications
, edited by
F. R.
Eirich
,
Academic Press
, NY, Vol.
1
.
2.
Green
,
A. E.
,
Adkins
,
J. E.
, 1960,
Large Elastic Deformation and Nonlinear Continuum Mechanics
,
Clarendon Press
, Oxford.
3.
Ogden
,
R. W.
, 1984,
Nonlinear Elastic Deformations
,
Ellis Horwood
, England.
4.
Beda
,
T.
,
Chevalier
,
Y.
, 2003, “
Hybrid Continuum Model for Large Elastic Deformation of Rubber
,”
J. Appl. Phys.
0021-8979,
94
(
4
), pp.
2701
2706
.
5.
Madsen
,
K.
,
Nielsen
,
H. B.
,
Tingleff
,
O.
, 1999, “
Method for Nonlinear Least Squares Problems
,” IMM, J. No H38, 7.7. 1999 HBN∕ms, TU Denmark.
6.
Kirkup
,
L.
, 2002, “
Principles and Applications of Non-Linear Least Squares: An Introduction for Physical Scientists Using Excel’s Solver
,”
UT Sydney, Science: Applied Physics
, Copyright UTS.
7.
Beda
,
T.
,
Chevalier
,
Y.
, 2003, “
Nonlinear Approximation Method by an Approach in Stages
,”
Comput. Mech.
0178-7675,
32
(
3
), pp.
177
184
.
8.
Beda
,
T.
, “
Combining Approach in Stages with Finite Domains Least Squares
” (to be published).
9.
Treloar
,
L. R. G.
, 1944, “
Stress–Strain Data for Vulcanized Rubber Under Various Types of Deformation
,”
Trans. Faraday Soc.
0014-7672,
40
, pp.
59
70
.
10.
Ogden
,
R. W.
, 1972a, “
Large Deformation Isotropic Elasticity—On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids
,”
Proc. R. Soc. London, Ser. A
1364-5021
326
, pp.
565
584
.
11.
Beda
,
T.
, 2005, “
Reconciling the Fundamental Phenomenological Expression of the Strain Energy of Rubber with Established Experimental Facts
,”
J. Polym. Sci., Part B: Polym. Phys.
0887-6266,
43
(
2
), pp.
125
134
.
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