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A Nitsche embedded mesh method. (English) Zbl 1366.74075
Summary: 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 F. P. T. Baaijens [Int. J. Numer. Methods Fluids 35, No. 7, 743–761 (2001; Zbl 0979.76044)]) 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.

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74A50 Structured surfaces and interfaces, coexistent phases
Full Text: DOI
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