Tuesday, 12 October 2004 - 9:40 AM

This presentation is part of : Rajagopal Symposium

A Rivlin Representation of the Strain Energy for Rubber

Michael, M Carroll, Rice Unniversity, Rice Unniversity, Department of Mechanical Engineering and Materials Science, MS 321, P.O. Box 1892, Houston, TX 77251-1892

In an earlier paper, a three-parameter strain energy function was shown to provide an excellent fit with data from the classic experiments of Treloar, Rivlin and Saunders, and Jones and Treloar. The strain energy has the Valanis-Landel form, with maximum allowable stretch, and it may also be represented as a function of the principal invariants of the stretch tensor. A Rivlin representation, i.e., a representation as a function of the principal invariants of the deformation tensor, is more convenient for solving boundary value problems. In the present paper, it is shown that such a representation may be obtained from the representation in terms of the stretch invariants by using the approach of Rivlin and Saunders, i.e., by examining the dependence of the partial derivatives of W on the principal deformation invariants. In effect, the theoretical strain energy, which is known to fit the data, is used to provide smoothed "data", thus avoiding the experimental error magnification that prevented Rivlin and Saunders from reaching a definitive conclusion as to the form of the strain energy function.

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