Finite Deformation Contact Based on a 3D Dual Mortar and Semi-Smooth Newton Approach

This paper gives a review of the recently proposed dual mortar approach combined with a consistently linearized semi-smooth Newton scheme for 3D finite deformation contact analysis. Some implementation aspects are presented in detail and the most important extensions of the contact model including friction and the treatment of self contact are highlighted. The mortar finite element method, which is applied as discretization scheme, initially yields a mixed formulation with the nodal Lagrange multiplier degrees of freedom as additional primary unknowns. However, by using so-called dual shape functions for Lagrange multiplier interpolation, the global linear system of equations to be solved within each Newton step can be condensed and thus contains only displacement degrees of freedom. All types of nonlinearities, including finite deformations, nonlinear material behavior and contact itself (active set search) are handled within one single iterative solution scheme based on a consistently linearized semi-smooth Newton method. Some very demanding numerical examples are presented to show the high quality of results obtained with this approach as well as to illustrate its superior numerical efficiency and robustness.