Dual mortar methods for computational contact mechanics - Overview and recent developments

Mortar-based finite element discretization in computational contact mechanics has seen a great thrust of research activities over the last years. In this contribution, we review the most important features of the so-called dual mortar finite element approach for finite deformation contact and friction. Advantageous properties of the devised algorithms comprise superior robustness as compared with the traditional node-to-segment (NTS) approach, the absence of any unphysical user-defined parameters (e.g. penalty parameter), the integration of all types of nonlinearities into one single iteration loop and the possibility to condense the biorthogonal discrete Lagrange multipliers from the global system of equations. Beside this general overview, some recent developments are highlighted, such as improved consistency and robustness of dual mortar methods, investigations on efficient numerical integration schemes, an extension to second-order interpolation as well as the combined treatment of contact and elastoplasticity. Several numerical examples are presented to illustrate the high quality of results obtained with the proposed methods.