The relation is established between the constitutive equations for the stress in an isotropic elastic material based on strain-energy functions that are functions of the right Cauchy-Green strain matrix and the right stretch matrix. It is shown that results to problems obtained on the basis of the latter can be simply obtained from those derived on the basis of the former.
[1] Ogden, R. W.Non-linear Elastic Deformations. Dover, New York, 1984.
2.
Reprinted in Collected Papers of R. S. Rivlin, Vol. 1, pp. 90-108, eds. G. I. Barenblatt and D. D. Joseph, Springer, New York, 1997.
3.
Reprinted in Collected Papers of R. S. Rivlin, Vol. 1, pp. 120-142, eds. G. I. Barenblatt and D. D. Joseph, Springer, New York, 1997.
4.
[4] Sawyers, K. N. and Rivlin, R. S.The strain-energy function for elastomers. Transactions of the Society of Rheology, 20, 545-557 (1976).
5.
[5] Sawyers, K. N.Comments on the paper “Determination of the stretch and rotation factors in the polar decomposition of the deformation gradient” by A. Hoger and D. E. Carlson. Quarterly Journal of Applied Mathematics, 44, 309-311 (1986).
6.
[6] Hoger, A. and Carlson, D. E.Determination of the stretch and rotation factors in the polar decomposition of the deformation gradient. Quarterly Journal of Applied Mathematics, 42, 113-117 (1984).
7.
[7] Ting, T. C. T.Determination of C½ and more general functions of C. J. Elasticity15, 319-323 (1985).
