Nonlinear coupled thermo-hyperelasticity analysis of thermal and mechanical wave propagation in a finite domain

In the present paper, a finite element nonlinear coupled thermo-hyperelasticity formulation is presented for analysis of the wave propagation, reflection, and mixing phenomena in an isotropic nearly incompressible finite length solid. The coupled equations are derived from the concept of large displacement and finite strain. In this regard, the second Piola–Kirchhoff stress and the full form of Green’s strain–displacement tensors are employed. The nonlinear equations are derived based on the idea of multiplicative decomposition of the deformation gradient. An appropriate strain–energy function is considered and by exchange the invariants of strain tensors in the modified model, the governing equations are extended to a nearly incompressible model. Strain–energy functions are selected based on polyconvexity conditions. In order to study the thermo-hyperelastic behavior, three terms including mechanical, thermal, and mechanical–thermal part are considered. The obtained results indicate that the term associated with the coupling of thermal and mechanical part, has a remarkable effects on thermal response of a body subjected to mechanical forces. Comparisons between elastic and thermal wave propagation in elastic and thermo-hyperelastic materials clarify that, unlike wave velocity, the amplitude of wave in thermo-hyperelastic material is significantly more than the elastic medium.