Isogeometric Mortar Methods for Optimal Weak Patch-Coupling and Contact Analysis in Finite Deformation Elasticity

Isogeometric Mortar Methods for Optimal Weak Patch-Coupling and Contact Analysis in Finite Deformation Elasticity

Robust and accurate contact discretization for nonlinear finite element analysis (FEA) has been an active field of research in the past decade, and a new class of formulations has emerged with the introduction of isogeometric analysis (IGA) based on non-uniform rational B-splines (NURBS). The high continuity of NURBS allows for a smooth surface representation, which makes their application to weak patch-coupling and contact analysis particularly appealing. At the same time, mortar methods have emerged as one the most promising and mathematically well-founded concepts to deal with non-conforming mesh- or patch-coupling and nonlinear frictional contact problems in the context of classical FEA. The aim of this work is to transfer the concept of so-called dual mortar methods from finite elements to IGA, thus for the first time combining the efficiency of dual mortar methods with the beneficial IGA inherent feature of a smooth geometry description. The newly developed formulations are applied to both patch-coupling (i.e. domain decomposition) and contact problems, and optimal spatial convergence properties of the discretization error are studied numerically by applying uniform mesh refinement in large-scale examples.