Modeling Cracks with a Partition of Unity Finite Element Method

John Dolbow, Northwestern University

Modeling cracks and crack growth with the finite element method is difficult due to the need for both the construction and regeneration of a fine mesh near the crack tip. We present a technique to enrich a standard displacement-based finite element approximation near a crack by incorporating a discontinuous field and the near tip asymptotic fields with a partition of unity method. In comparison to modeling the crack geometrically with the mesh, the crack is modeled physically with the special enrichment functions. This technique provides for both coarse mesh accuracy and arbitrary crack alignment within the mesh. Crack growth is modeled in a straightforward fashion by redefining the physical extent of the discontinuity: no remeshing is necessary. The advantages of the present technique over meshless and boundary element methods are discussed. Several example problems of fracture in two dimensional elasticity and Mindlin-Reissner plates are provided to illustrate the accuracy and utility of the new formulation.

Abstract Author(s): John Dolbow