Extended finite element method for three-dimensional crack modelling

TLDR

The paper describes an extended finite element method (X‑FEM) for three‑dimensional crack modelling. The method enriches the finite element approximation with a discontinuous function and two‑dimensional asymptotic crack‑tip displacement fields via partition of unity, allowing three‑dimensional domains to be modeled without explicit crack‑surface meshing and addressing associated computational geometry issues. Stress intensity factors for planar three‑dimensional cracks are computed and found to agree well with benchmark solutions. © 2000 John Wiley & Sons, Ltd.

Abstract

An extended finite element method (X-FEM) for three-dimensional crack modelling is described. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Stress intensity factors (SIFs) for planar three-dimensional cracks are presented, which are found to be in good agreement with benchmark solutions. Copyright © 2000 John Wiley & Sons, Ltd.