In the first part of this paper a pressure projection method was presented for the nonlinear analysis of structures made of nearly incompressible hyperelastic materials. The main focus of the second part of the paper is to demonstrate the performance of the present method and to address some of the issues related to the analysis of engineering elastomers including the proper selection of strain energy density functions. The numerical procedures and the implementation to nonlinear finite element programs are presented. Mooney-Rivlin, Cubic, and Modified Cubic strain energy density functions are used in the numerical examples. Several classical finite elasticity problems as well as some practical engineering elastomer problems are analyzed. The need to account for the slight compressibility of rubber (finite bulk modulus) in the finite element formulation is demonstrated in the study of apparent Young’s modulus of bonded thin rubber units. The combined shear-bending deformation that commonly exists in rubber mounting systems is also analyzed and discussed.

1.
Chang
T. Y. P.
,
Saleeb
A. F.
, and
Li
G.
,
1991
, “
Large Strain Analysis of Rubber-like Materials Based on a Perturbed Lagrangian Variational Principle
,”
Computational Mechanics
, Vol.
8
, pp.
221
233
.
2.
Chen
J. S.
, and
Pan
C.
,
1996
, “
A Pressure Projection Method for Nearly Incompressible Rubber Hyperelasticity, Part I: Theory
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
63
, pp.
862
868
.
3.
Gent
A. N.
, and
Lindley
P. B.
,
1959
, “
The Compression of Bonded Rubber Blocks
,”
Proceedings of the Institution of Mechanical Engineers
, Vol.
173
, pp.
111
122
.
4.
Gent
A. N.
, and
Meinecke
E. A.
,
1970
, “
Compression, Bending and Shear of Bonded Rubber Blocks
,”
Polymer Engineering and Science
, Vol.
10
, pp.
48
53
.
5.
James
A. G.
,
Green
A.
, and
Simpson
G. M.
,
1975
a, “
Strain Energy Functions of Rubber. I. Characterization of Gum Rubber
,”
Journal of Applied Polymer Science
, Vol.
19
, pp.
2033
2058
.
6.
James
A. G.
, and
Green
A.
,
1975
b, “
Strain Energy Functions of Rubber. II. The Characterization of Filled Vulcanizates
,”
Journal of Applied Ploymer Science
, Vol.
19
, pp.
2319
2330
.
7.
Liu
W. K.
,
Belytschko
T.
, and
Chen
J. S.
,
1988
, “
Nonlinear Versions of Flexurally Superconvergent Elements
,”
Computer Methods in Applied Mechanics and Engineering
, Vol.
71
, pp.
241
256
.
8.
Payne, A. R., 1957, “Dynamic Properties of Vulcanized Rubber: 5. Shape Factors and Functions in Rubber Engineering,” Research Association of British Rubber Manufactures, Research Report No. 84, Shawbury.
9.
Rivlin
R. S.
,
1949
, “
Large Elastic Deformation of Isotropic Materials, Part VI, Further Results in the Theory of Torsion, Shear and Flexure
,”
Philosophical Transactions of the Royal Society of London
, Vol.
A242
, pp.
173
195
.
10.
Rivlin, R. S., 1956, “Rheology Theory and Applications,” F. R. Eirich, ed., Academic Press, New York, Vol. 1, Chapter 10, pp. 351–385.
11.
Rivlin, R. S., and Saunders, D. W., 1951, “Large Elastic Deformation of Isotropic Materials. Part 7, Experiments on the Deformation of Rubber,” Philosophical Transactions of the Royal Society of London, Vol. A243, pp. 251–288.
12.
Rivlin
R. S.
, and
Saunders;
D. W.
,
1949
, “
Cylindrical Shear Mountings
,”
Transactions, I.R.I
, Vol.
24
, p.
296
296
.
13.
Scharnhorst
T.
, and
Pian
T. H. H.
,
1978
, “
Finite Element Analysis of Rubber-like Materials by a Mixed Model
,”
International Journal for Numerical Methods in Engineering
, Vol.
12
, pp.
665
676
.
14.
Tschoegl
N. W.
,
1971
, “
Constitutive Equations for Elastomers
,”
Journal of Applied Ploymer Science
, Vol.
A1
, pp.
1959
1970
.
15.
Tseng, N.T., Satyamurthy, K., and Chang, J. P., 1987, “Nonlinear Finite Element Analysis of Rubber Based Products,” The 131st Meeting of the Rubber Division, American Chemical Society, Montreal, Quebec, Canada, May 26-29.
16.
Yeoh
O. H.
,
1990
, “
Characterization of Elastic Properties of Carbon Black Filled Rubber Vulcanizates
,”
Rubber Chemistry and Technology
, Vol.
63
, pp.
792
805
.
17.
Yeoh
O. H.
,
1993
, “
Some Forms of the Strain Energy Function for Rubber
,”
Rubber Chemistry and Technology
, Vol.
66
, pp.
754
771
.
18.
Yeoh, O. H., 1994, personal communication.
This content is only available via PDF.
You do not currently have access to this content.