Stable 3D XFEM/vector level sets for non‐planar 3D crack propagation and comparison of enrichment schemes

TLDR

The study presents a 3‑D vector level set method coupled to a stable XFEM and investigates a new enrichment approach using discontinuous linear functions instead of asymptotic near‑tip functions. The method employs a vector level set to obtain crack geometry via simple geometric operations, avoiding differential evolution equations, and applies geometrical enrichment with enriched elements in a fixed volume around the crack front, tested with two discretization schemes for nonplanar crack propagation. The geometrical enrichment variant achieves optimal convergence without conditioning issues, while the linear enrichment simplifies implementation and reduces integration cost, yielding nonoptimal convergence comparable to standard FEM; both schemes were validated on benchmark problems and nonplanar crack propagation.

Abstract

Summary We present a three‐dimensional vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting discontinuous linear enrichment functions in place of the asymptotic near‐tip functions. Through the vector level set method, level set values for propagating cracks are obtained via simple geometrical operations, eliminating the need for solution of differential evolution equations. The first XFEM variant ensures optimal convergence rates by means of geometrical enrichment, ie, the use of enriched elements in a fixed volume around the crack front, without giving rise to conditioning problems. The linear enrichment approach, significantly simplifies implementation and reduces the computational cost associated with numerical integration, while providing nonoptimal convergence rates similar to standard finite elements. The 2 dicretization schemes are tested for different benchmark problems, and their combination to the vector level set method is verified for nonplanar crack propagation problems.