A Partition of Unity Finite Element Method for Cohesive Zone Modeling of Fracture

Speaker: James V. Cox,
Advanced Mechanics Development Department,
Sandia National Laboratories,
Albuquerque, New MexicoAbstract:Meaningful computational investigations of many solid mechanics problems require accurate characterization of material behavior through failure. A recent approach to fracture modeling has combined the partition of unity finite element method (PUFEM) with cohesive zone models. In the PUFEM, the displacement field is enriched to improve the local approximation. Previous studies have used simplified enrichment functions to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack. In this study enrichment functions based upon two existing analytical investigations of the cohesive crack problem are proposed. These functions have the potential of representing displacement gradients in the vicinity of the cohesive crack with a relatively coarse mesh and allow the crack to incrementally advance across each element. An overview of the enrichment functions and key aspects of the numerical implementation are presented. Analysis results for simple model problems are presented to evaluate if quasi-static crack propagation can be accurately followed with the proposed formulation. A standard finite element solution with interface elements is used to provide the accurate reference solution, so the model problems are limited to a straight, mode I crack in plane stress. Except for the cohesive zone, the material model for the problems is homogenous, isotropic linear elasticity. Propagation of the cohesive zone tip and crack tip, time variation of the cohesive zone length, and crack profiles are examined to assess the potential of this PUFEM. The effects of mesh refinement and mesh orientation on the results are also considered. The analysis results indicate that the enrichment functions based upon the asymptotic solutions can accurately track the cohesive crack propagation independent of mesh orientation. Extension of the formulation to mixed mode cracking and applicability of the enrichment functions to problems with inelastic domains are the subjects of ongoing studies.

Location: Kaprielian Hall (KAP) - rielian Hall 209

Audiences: Everyone Is Invited

Contact: Evangeline Reyes