State-of-the-Art Computational Methods for Finite Deformation Contact Modeling of Solids and Structures

In this contribution, we review mortar finite element methods (FEM), which are nowadays the most well-established computational technique for contact modeling of solids and structures in the context of finite deformations and frictional sliding. Based on some concepts of nonlinear continuum mechanics, the mortar approach is first presented for the more accessible case of mesh tying (also referred to as tied contact). Mortar methods for unilateral contact then follow in a rather straightforward manner, despite the fact that several complexities, such as inequality constraints, are added to the problem formulation. A special focus is set on practical aspects of the implementation of mortar methods within a fully nonlinear, 3D finite element environment. Specifically, the choice of suitable discrete Lagrange multiplier bases, aspects of high performance computing (HPC), numerical integration procedures and new discretization techniques such as isogeometric analysis (IGA) using NURBS are discussed. Eventually, the great potential of mortar methods in the more general field of computational interface mechanics is exemplified through applications such as wear modeling and coupled thermo-mechanical interfaces.