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The Discontinuity‐Enriched Finite Element Method
Author(s) -
Aragón Alejandro M.,
Simone Angelo
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5570
Subject(s) - finite element method , classification of discontinuities , discontinuity (linguistics) , polygon mesh , extended finite element method , discretization , mathematics , traction (geology) , context (archaeology) , mixed finite element method , degrees of freedom (physics and chemistry) , finite element limit analysis , mathematical analysis , geometry , structural engineering , engineering , physics , mechanical engineering , geology , paleontology , quantum mechanics
Summary We introduce a new methodology for modeling problems with both weak and strong discontinuities independently of the finite element discretization. At variance with the eXtended/Generalized Finite Element Method (X/GFEM), the new method, named the Discontinuity‐Enriched Finite Element Method (DE‐FEM), adds enriched degrees of freedom only to nodes created at the intersection between a discontinuity and edges of elements in the mesh. Although general, the method is demonstrated in the context of fracture mechanics, and its versatility is illustrated with a set of traction‐free and cohesive crack examples. We show that DE‐FEM recovers the same rate of convergence as the standard FEM with matching meshes, and we also compare the new approach to X/GFEM.