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 formulation 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 numerical 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 computational 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 associated with actual unilateral contact formulation but, on the other hand, clarify many of the conceptual and implementational aspects of the contact mechanics.