Nitsche’s method for finite deformation thermomechanical contact problems

This paper presents an extension of Nitsche’s method to finite deformation thermomechanical contact problems including friction. The mechanical contact constraints, i.e. non-penetration and Coulomb’s law of friction, are introduced into the weak form using a stabilizing consistent penalty term. The required penalty parameter is estimated with local generalized eigenvalue problems, based on which an additional harmonic weighting of the boundary traction is introduced. A special focus is put on the enforcement of the thermal constraints at the contact interface, namely heat conduction and frictional heating. Two numerical methods to introduce these effects are presented, a substitution method as well as a Nitsche-type approach. Numerical experiments range from two-dimensional frictionless thermo-elastic problems demonstrating optimal convergence rates to three-dimensional thermo-elasto-plastic problems including friction.