Toward robust and accurate contact solvers for large deformation applications: a remapping/adaptivity framework for mortar-based methods

In recent years, the mortar method has proven to be an effective spatial discretization strategy for large deformation contact problems, particularly when such problems feature deformable-to-deformable contact. The mortar approach has been shown to greatly enhance both the spatial accuracy and the robustness with which such problems can be solved in many circumstances. In this work, we concern ourselves with problems that arise in the context of many practical applications, both in manufacturing and in other areas. Specifically, it is frequently necessary to remesh a problem in the midst of an ongoing incremental loading strategy, either because of adaptive mesh refinement being used to improve resolution, or excessive mesh distortion which necessitates an overall remeshing. This work focuses on a particularly important issue associated with contact remeshing; i.e., the remapping of contact variables after the remesh so that a simulation can successfully continue. We develop and demonstrate our algorithm in the context of a mortar-discretized approach to contact. The approach is applicable to either two or three dimensional analysis, and is demonstrated by a number of three dimensional numerical examples.