Comparison of Incompressible Elastic Strain Energy Functions over the Attainable Region of Invariant Space

Abstract

Within the theory of isothermal, homogeneous, isotropic, nonlinear elasticity, the selection of the appropriate form for the strain energy function is still an issue. Over the years, a number of proposals have been made for specific strain energy functions, some based on experimental data, others based on mathematical elegance or specific theoretical constraints. Because of differing formulations, it is difficult to compare strain energy functions. In this paper, methods first introduced by Haines and Wilson are used to compare incompressible strain energy functions, and these methods are applied to a number of models from the literature, including six which have been correlated with the 1944 data of Treloar. Comparison is made easier by the fact that the value of the strain energy function is relevant only over a limited region of invariant space, known as the attainable region. The comparison shows that four of the models predict similar strain energy functions up to moderate strains, but that they do not reproduce all of the characteristics of the original experimental data.