Mortar Methods for Single- and Multi-Field Applications in Computational Mechanics

Mortar finite element methods are of great relevance as a non-conforming discretization technique in various single-field and multi-field applications. In computational contact analysis, the mortar approach allows for a variationally consistent treatment of non-penetration and frictional sliding constraints despite the inevitably non-matching interface meshes. Other single-field and multi-field problems, such as fluid–structure interaction (FSI), also benefit from the increased modeling flexibility provided by mortar methods. This contribution gives a review of the most important aspects of mortar finite element discretization and dual Lagrange multiplier interpolation for the aforementioned applications. The focus is on parallel efficiency, which is addressed by a new dynamic load balancing strategy and tailored parallel search algorithms for computational contact mechanics. For validation purposes, simulation examples from solid dynamics, contact dynamics and FSI will be discussed.