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An extended/generalized phase‐field finite element method for crack growth with global‐local enrichment
Author(s) -
Geelen Rudy,
Plews Julia,
Tupek Michael,
Dolbow John
Publication year - 2020
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.6318
Subject(s) - quasistatic process , discretization , extended finite element method , finite element method , benchmark (surveying) , displacement field , mathematics , displacement (psychology) , field (mathematics) , structural engineering , mathematical optimization , computer science , mathematical analysis , engineering , physics , geology , psychology , geodesy , quantum mechanics , pure mathematics , psychotherapist
Summary An extended/generalized finite element method (XFEM/GFEM) for simulating quasistatic crack growth based on a phase‐field method is presented. The method relies on approximations to solutions associated with two different scales: a global scale, that is, structural and discretized with a coarse mesh, and a local scale encapsulating the fractured region, that is, discretized with a fine mesh. A stable XFEM/GFEM is employed to embed the displacement and damage fields at the global scale. The proposed method accommodates approximation spaces that evolve between load steps, while preserving a fixed background mesh for the structural problem. In addition, a prediction‐correction algorithm is employed to facilitate the dynamic evolution of the confined crack regions within a load step. Several numerical examples of benchmark problems in two‐ and three‐dimensional quasistatic fracture are provided to demonstrate the approach.