A Primal-Dual Active Set Strategy for Finite Deformation Dual Mortar Contact

The numerical simulation of contact problems in the context of finite deformation elasticity is considered. We present an approach based on mortar finite element discretization and use a primal-dual active set strategy for direct constraint enforcement. So-called dual Lagrange multiplier spaces are introduced such that a condensation of the global system of equations can be performed, thus avoiding an undesirable increase in system size. Both linear and quadratic shape functions are addressed and we exemplify the method for the 2D frictionless case. First and foremost, a full linearization of the dual mortar approach is provided in order to derive a consistent Newton scheme for the iterative solution of the nonlinear system. By further interpreting the active set search as a semi-smooth Newton method, contact nonlinearity and geometrical and material nonlinearity can be treated within one single iterative scheme. This yields a robust and highly efficient algorithm for finite deformation contact problems without regularization of the contact constraints.