Adaptive Methods for Contact Problems

Abstract

This contribution is concerned with the adaptive finite-element-formulation of contact problems. For this, first the theoretical background of continuum mechanics and contact kinematics is given. Next the basic finite element formulation for large deformation contact processes is presented for two-dimensional problems. The development of the discretization of contact contributions follows. Here standard approaches are discussed for the case of frictional and frictionless contact. Finally different adaptive strategies involving as well residual based error estimators as error indicators based on superconvergence patch recovery are derived and formulated to include the contributions due to contact. Also error estimators based on dual principles are discussed. Examples show the performance of the different formulations and adaptive strategies.