Towards an Extrinsic, CG-XFEM Approach Based on Hierarchical Enrichments for Modeling Progressive Fracture

by   M. Keith Ballard, et al.

We propose an extrinsic, continuous-Galerkin (CG), extended finite element method (XFEM) that generalizes the work of Hansbo and Hansbo to allow 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 CG 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.


page 17

page 24

page 31

page 32

page 34


Unified Implementation of Adaptive Finite Element Methods in Matlab

We provide a unified implementation of the adaptive finite element metho...

De Rham Complexes for Weak Galerkin Finite Element Spaces

Two de Rham complex sequences of the finite element spaces are introduce...

An open-source ABAQUS implementation of the scaled boundary finite element method to study interfacial problems using polyhedral meshes

The scaled boundary finite element method (SBFEM) is capable of generati...

Algorithms for Parallel Generic hp-adaptive Finite Element Software

The hp-adaptive finite element method (FEM) - where one independently ch...

On the Design of Locking Free Ghost Penalty Stabilization and the Relation to CutFEM with Discrete Extension

In this note, we develop a new stabilization mechanism for cut finite el...

Intrinsic Integration

If we wish to integrate a function h|Ω⊂^n→ along a single T-level surfac...

Probabilistic Modeling of Progressive Filtering

Progressive filtering is a simple way to perform hierarchical classifica...

Please sign up or login with your details

Forgot password? Click here to reset