A MORTAR BASED CONTACT FORMULATION FOR NON-LINEAR DYNAMIC PROBLEMS USING DUAL LAGRANGE MULTIPLIERS

Summary. This work presents a large deformation contact formulation for non-linear dynamic problems. The formulation is based on the mortar method and uses dual spaces for the interpola- tion of the Lagrange multiplier. A local basis transformation in combination with a primal-dual active set strategy allows a nodal decoupling of the contact constraints. 1I NTRODUCTION Many existing algorithms for the analysis of large deformation contact problems use a so- called node-to-segment approach to discretize the contact interface between dissimilar meshes. It is well known, that this discretization strategy may lead to problems like loose of convergence or jumps in the contact forces. Additionally it is popular to use penalty methods to satisfy the contact constraints. This necessitates a user defined penalty parameter, the choice of which is somehow arbitrary, problem dependent and might influence the accuracy of the analysis. In this work, a segment-to-segment contact formulation is presented, that does not require any user defined parameter to handle the non-linearity of the contact conditions. The approach is based on the mortar method, enforcing the compatibility condition along the contact interface in a weak integral sense.