A mortar based contact formulation for non-linear dynamics using dual Lagrange multipliers

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 loss 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 frictionless 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. The application of dual spaces for the interpolation of the Lagrange multiplier allows for a nodal decoupling of the contact constraints. A local basis transformation in combination with a primal-dual active set strategy enables the exact enforcement of the contact constraints via prescribed incremental boundary conditions. Due to the biorthogonality condition of the basis functions the Lagrange multipliers can be locally eliminated. A static condensation leads to a reduced system of equations to be solved solely for the unknown nodal displacements. Thus the size of the system of equations remains constant during the whole calculation. The discrete Lagrange multipliers, representing the contact pressure, can be easily recovered from the displacements in a variationally consistent way. For the analysis of dynamic contact problems the proposed contact description is combined with the implicit Generalized Energy-Momentum Method. Several numerical examples illustrate the performance of the suggested contact formulation.