Adaptive methods for thermomechanical coupled contact problems

In this paper an adaptive method for the analysis of thermomechanical coupled multi-body contact problems is presented. The method is applied to non-linear elastic solids undergoing finite (thermal) deformations. The contact model considers non-linear pressure-dependent heat flux as well as frictional heating in the interface. A time–space-finite element discretization of the governing equations is formulated including unilateral constraints due to contact. A staggered solution algorithm has been constructed that allows an independent spatial discretization of the coupled subproblems. A posteriori projection-based error estimators, which enforce implicitly the special boundary conditions due to thermal contact, are used to control the spatial discretization as well as the adaptive time stepping. Numerical examples are presented to corroborate the applicability of the adaptive algorithm to the considered problem type