On Spatial vs Referential Isotropic Fourier’s Law in Finite Deformation Thermomechanics

This paper deals with the issue of isotropic heat conduction in thermomechanical large-strain problems. The aim of the paper is a comparison of different variants of Fourier’s law used in the literature for a large strain problem. In particular, Fourier’s law is specified either in the reference or in the deformed configuration by using different options of heat flux density vectors which are presented and discussed. The paper includes working examples to illustrate the presented theory. Moreover, different formulations of Fourier’s law are tested by using the finite element method to investigate the influence of the applied variant on simulation results. The analysis reveals that in a strongly deformed area the temperature distribution varies.