Three-dimensional mortar contact formulation: an efficient and accurate numerical implementation

The mortar contact formulation is a well-established technique to tie non-conforming finite element meshes in domain decomposition and is also the basis of many well-known contact algorithms. Mortar contact formula- tion allows for a variationally consistent treatment of contact conditions including mesh tying, non-penetration, frictionless and frictional sliding leading to satisfaction of contact patch test. Efficient, accurate and robust nu- merical implementation of the interface coupling terms associated with the mortar contact formulation remains challenging, especially in three-dimensional case. The computational contact algorithm presented in this paper is carefully designed for accuracy, efficiency and robustness and making use of the cutting-edge third-party computa- tional tools including Mesh-Oriented datABase (MOAB), Portable, Extensible Toolkit for Scientific Computation (PETSc), Boost and clipper libraries. The computational framework is designed to take advantage of distributed memory high-performance computing and hierarchic basis functions. The numerical implementation is validated with two non-conforming mesh tying examples, which, on the one hand, remove some of the complexities as- sociated with actual unilateral contact formulation but, on the other hand, clarify many of the conceptual and implementational aspects of the contact mechanics.