Stabilized MorteX method for mesh tying along embedded interfaces
| Autor: | Akula, Basava Raju, Vignollet, Julien, Yastrebov, Vladislav A. |
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| Přispěvatelé: | Safran Tech, Centre des Matériaux (MAT), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
MorteX method Computer Science - Numerical Analysis [PHYS.MECA.GEME]Physics [physics]/Mechanics [physics]/Mechanical engineering [physics.class-ph] embedded interface Numerical Analysis (math.NA) X-FEM [PHYS.MECA.MSMECA]Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph] mortar method stabilization Computational Engineering Finance and Science (cs.CE) mesh tying [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph] FOS: Mathematics Mathematics - Numerical Analysis Computer Science - Computational Engineering Finance and Science [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] ComputingMethodologies_COMPUTERGRAPHICS |
| Popis: | We present a unified framework to tie overlapping meshes in solid mechanics applications. This framework is a combination of the X-FEM method and the mortar method, which uses Lagrange multipliers to fulfill the tying constraints. As known, mixed formulations are prone to mesh locking which manifests itself by the emergence of spurious oscillations in the vicinity of the tying interface. To overcome this inherent difficulty, we suggest a new coarse-grained interpolation of Lagrange multipliers. This technique consists in selective assignment of Lagrange multipliers on nodes of the mortar side and in non-local interpolation of the associated traction field. The optimal choice of the coarse-graining spacing is guided solely by the mesh-density contrast between the mesh of the mortar side and the number of blending elements of the host mesh. The method is tested on two patch tests (compression and bending) for different interpolations and element types as well as for different material and mesh contrasts. The optimal mesh convergence and removal of spurious oscillations is also demonstrated on the Eshelby inclusion problem for high contrasts of inclusion/matrix materials. Few additional examples confirm the performance of the elaborated framework. 32 pages, 36 figures, 64 references |
| Databáze: | OpenAIRE |
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