Entropic thermoelasticity at finite strains. Aspects of the formulation and numerical implementation Original Research Article

This paper presents a formulation of isotropic finite strain thermoelasticity and addresses some aspects of its numerical implementation. On the theoretical side, a Eulerian setting of isotropic thermoelasticity is discussed, based on the Finger tensor as a strain measure. Novel aspects are a direct representation of the Eulerian thermoelastic moduli in terms of the Finger tensor and a rigorous decomposition of the thermoelastic response functions into decoupled volumetric and isochoric contributions based on a multiplicative split of the Finger tensor into spherical and unimodular parts. An algorithmic procedure for the computation of the stress and thermoelastic moduli, based on a representation of the free energy in terms of eigenvalues of the unimodular part of the Finger tensor, is developed and applied to model problems of strictly entropic and modified entropic thermoelasticity. Furthermore, two algorithms for the solution of the coupled problem are discussed, based on operator splits of the global field equations of thermoelasticity. The paper concludes with some representative numerical simulations of thermoelastic processes in rubber-like materials.