Towards an extrinsic, CG-XFEM approach based on hierarchical enrichments for modeling progressive fracture

• Published in: Computer methods in applied mechanics and engineering 2022-01, Vol.388, p.114221, Article 114221
• Main Authors: Ballard, M. Keith, Amici, Roman, Shankar, Varun, Ferguson, Lauren A., Braginsky, Michael, Kirby, Robert M.
• Format: Article
• Language: English
• Subjects: Algorithms; CG-XFEM; Computer networks; Degrees of freedom; Distributed processing; Enrichment; Enumeration; Finite element method; Heaviside enrichment; HHE; Hierarchies; Mathematical analysis; Mathematical models; Numerical integration; Progressive fracture; Software; Strain
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2021.114221

We propose an extrinsic, continuous-Galerkin (CG), extended finite element method (XFEM) that allows multiple Heaviside enrichments within a single element in a hierarchical manner. This approach enables complex, evolving XFEM surfaces in 3D that cannot be captured using existing CG-XFEM approaches. We describe an implementation of the method for 3D static elasticity with linearized strain for modeling open cracks as a salient step towards modeling progressive fracture. The implementation includes a description of the finite element model, hybrid implicit/explicit representation of enrichments, numerical integration method, and novel degree-of-freedom (DoF) enumeration algorithm. This algorithm supports an arbitrary number of enrichments within an element, while simultaneously maintaining a continuous solution across elements. Additionally, our approach easily allows an implementation suitable for distributed computing systems. Enabled by the DoF enumeration algorithm, the proposed method lays the groundwork for a computational tool that efficiently models progressive fracture. To facilitate a discussion of the complex enrichment hierarchies, we develop enrichment diagrams to succinctly describe and visualize the relationships between the enrichments (and the fields they create) within an element. This also provides a unified language for discussing extrinsic XFEM methods in the literature. We compare several methods, relying on the enrichment diagrams to highlight their nuanced differences. •Presents the foundation of a new approach for simulating progressive fracture.•Models cracks and/or bi-material interfaces that do not conform to the mesh.•Allows multiple discontinuities in an element in a hierarchical fashion.•Easily parallelizable and suitable for distributed computing implementations.