Some aspects of thermodynamic effects in finite amplitude wave propagation in rubber-like solids

Abstract

In this study, we apply the modified entropic elasticity theory to investigate the thermodynamic effects in finite amplitude wave propagation in a stretched hyperelastic string. In formulating the problem, we assume that the string is composed of a non-conducting rubber-like material, and that the deformation is isochoric. Adiabatic stress–stretch relations are obtained for strictly entropic and piezotropic materials, which are the two limiting cases of modified entropic elasticity. The Lagrangian system of governing equations for finite amplitude wave propagation in a stretched hyperelastic string is derived in conservation form. Similarity solutions are presented for two strain energy functions. The errors in adopting an isothermal stress–stretch relation instead of an adiabatic stress–stretch relation, and the validity of the isentropic approximation, are investigated. The treatise developed in this study, and the results obtained, appear to be new.