A fast solver for finite deformation contact problems

Abstract

We present a new solver for large-scale two-body contact problems in nonlinear elasticity. It is based on an SQP-trust-region approach. This guarantees global convergence to a first-order critical point of the energy functional. The linearized contact conditions are discretized using mortar elements. A special basis transformation known from linear contact problems allows to use a monotone multigrid solver for the inner quadratic programs. They can thus be solved with multigrid complexity. Our algorithm does not contain any regularization or penalization parameters, and can be used for all hyperelastic material models.