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Modeling holes and inclusions by level sets in the extended finite element method. (English) Zbl 1029.74049
Summary: We propose a methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries. The numerical method couples the level set method to the extended finite element method (X-FEM). In the X-FEM, the finite element approximation is enriched by additional functions through the notion of partition of unity. The level set method is used for representing the location of holes and material interfaces, and in addition the level set function is used to develop the local enrichment for material interfaces. Numerical examples in two-dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
74E05 Inhomogeneity in solid mechanics
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