A Nitsche embedded mesh method

A new technique for treating the mechanical interactions of overlapping finite element meshes is proposed. Numerous names have been applied to related approaches, here we refer to such techniques as embedded mesh methods. Such methods are useful for numerous applications e. g., fluid-solid interaction with a superposed meshed solid on an Eulerian background fluid grid or solid-solid interaction with a superposed meshed particle on a matrix background mesh etc. In this work we consider the interaction of two elastic domains: one mesh is the foreground and defines the surface of interaction, the other is a background mesh and is often a grid. We first employ a classical mortar type approach [see Baaijens (Int J Numer Methods Eng 35: 743-761, 2001)] to impose constraints on the interface. It turns out that this approach will work well except in special cases. In fact, many related approaches can exhibit mesh locking under certain conditions. This motivates the proposed version of Nitsche's method which is shown to eliminate the locking phenomenon in example problems.