Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 91, Issue 3, Pages 289-305Publisher
WILEY
DOI: 10.1002/nme.4265
Keywords
discontinuous Galerkin; Nitsche's method; embedded grids; mesh locking
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A new technique for treating the mechanical interactions of overlapping finite element meshes is presented. Such methods can be useful for numerous applications, for example, fluidsolid interaction with a superposed meshed solid on an Eulerian background fluid grid. 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 structured grid. Many of the previously proposed methods employ surface defined Lagrange multipliers or penalties to enforce the boundary constraints. It has become apparent that these methods will cause mesh locking under certain conditions. Appropriately applied, the Nitsche method can overcome this locking, but, in its canonical form, is generally not applicable to non-linear materials such as hyperelastics. The relationship between interior point penalty, discontinuous Galerkin and Nitsche's method is well known. Based on this relationship, a nonlinear theory analogous to the Nitsche method is proposed to treat nonlinear materials in an embedded mesh. Here, a discontinuous Galerkin derivative based on a lifting of the interface surface integrals provides a consistent treatment for non-linear materials and demonstrates good behavior in example problems. Published 2012. This article is a US Government work and is in the public domain in the USA.
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