The relaxation effects of volume properties in two-dimensional generalized thermoviscoelastic problem

Abstract

This paper deals with the two-dimensional generalized thermoviscoelastic problem with two relaxation times taking into consideration the rheological properties of the volume in material having temperature-dependent properties. The results obtained are used to look for the exact expressions of the temperature distribution, thermal stresses and the displacement components in the Fourier transformed domain, assuming that these expressions are sufficiently smooth such that the normal mode analysis of these functions exist. The technique is applied to two different concrete problems. The first deals with a thick plate subjected to a time-dependent heat source on each face, the second concerns the case of a heated punch moving across the surface of an infinite thermoelastic space subjected to appropriate boundary conditions. Numerical results are given and illustrated for both problems. Comparisons are made with the results predicted ignoring rheological properties of the volume, or the temperature-dependence of the mechanical properties, or by the coupled theory.