An extended/generalized phase‐field finite element method for crack growth with global‐local enrichment

• Published in: International journal for numerical methods in engineering Vol. 121; no. 11; pp. 2534 - 2557
• Main Authors: Geelen, Rudy, Plews, Julia, Tupek, Michael, Dolbow, John
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 15.06.2020; Wiley Blackwell (John Wiley & Sons)
• Subjects: Algorithms; Computer simulation; crack growth; Crack propagation; Discretization; extended/generalized FEM; Finite element analysis; Finite element method; global‐local analysis; gradient damage models; multiscale; phase‐fields
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6318

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.