On the fully coupled quasi-static equations for the thermoelastic halfspace

Abstract

Influence functions for fully coupled quasi-static thermoelasticity are presented. They can be used to calculate displacements, stresses as well as temperature distributions within a halfspace for arbitrarily shaped and time dependent heat sources or pressure distributions on the surface. To this end, the underlying equations are solved for a mechanically or thermally loaded rectangular element on the surface by potential theory. The solution procedure is described in detail. The obtained results are verified and may easily be transferred to the theory of poroelasticity where the underlying equations are structurally equal. Example calculations for a parabolic pressure field, heat flux and temperature field are performed and simulation results are discussed particularly in comparison to the uncoupled case. Estimations of the extent to which the Gough–Joule effect and its consequences can be neglected are given.