A Multiscale strategy in XFEM with xed enrichment Area for 2D crack problems Under tensile load

Abstract

The eXtended Finite Element Method (XFEM) is one of the most effective methods to solve the crack growth problems without remeshing. In the XFEM, the mesh is discretized independently from the geometry of crack, and the elements containing the crack will be defined by a level set method. A standard displacement-based field is approximated and enriched near the crack by incorporating both discontinuous field and the near tip asymptotic field through a partition of unity method. The method, however, still requires a fine mesh in the vicinity of the crack tip to ensure the accuracy. In addition, when crack propagation occurs, the crack tip will reach coarse-meshed domain and the accuracy will tend to decrease significantly. A multiscale strategy hence is necessary to be incorporated with the XFEM to ensure the accuracy when the crack propagates. From the original mesh, a fixed subdomain of enriched elements near the crack is chosen to refine, and a static condensation technique in computing will be used to connect the refined suddomain with the original mesh.. This paper gave out some results archived by using Multiscale XFEM with fixed enrichment area for 2D crack problems under tensile load.

Key words: Multiscale strategy, X-FEM, crack propagation, Level sets, enrichment function