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Title:
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Stability of incompressible formulations enriched with X-FEM
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Author:
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Legrain, G; Moes, N; Huerta, Antonio
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
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Abstract:
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The treatment of (near-)incompressibility is a major concern for applications involving rubber-like materials, or when important plastic ows occurs as in forming processes. The use of mixed nite element methods is known to prevent the locking of the nite element approximation in the incompressible limit. However, it also introduces a critical condition for the stability of the formulation, called the infsup or LBB condition. Recently, the nite element method has evolved with the introduction of the partition of unity. The eXtended Finite Element Method (XFEM) uses the partition of unity to remove the need to mesh physical surfaces or to remesh them as they evolve. The enrichment of the displacement eld makes it possible to treat surfaces of discontinuity inside nite elements. In this paper, some strategies are proposed for the enrichment of mixed nite element approximations in the incompressible setting. The case of holes, material interfaces and cracks are considered. Numerical examples show that for well chosen enrichment strategies, the nite element convergence rate is preserved and the inf-sup condition is passed. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
-Incompressibility
-Finite element method
-Elements finits, Mètode dels -- Mecànica de fluids |
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Rights:
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Document type:
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Article - Submitted version
Article |
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