An analytically enriched finite element method for cohesive crack modeling.
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. Extension of the PUFEM to address crack propagation is often referred to as the extended finite element method (XFEM). In the PUFEM, the displacement field is enriched to improve the local approximation. Most XFEM studies have used simplified enrichment functions (e.g., generalized Heaviside functions) to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack. As such, the mesh had to be sufficiently fine for the FEM basis functions to capture these gradients.In this study enrichment functions based upon two analytical investigations of the cohesive crack problem are examined. 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. Key aspects of the corresponding numerical formulation are summarized. 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. The effects of mesh refinement, mesh orientation, and enrichment schemes that enrich a larger region around the cohesive crack are considered in the study. Propagation of the cohesive zone tip and crack tip, time variation of the cohesive zone length, and crack profiles are presented. The analysis results indicate that the enrichment functions based upon the asymptotic solutions can accurately track the cohesive crack propagation independent of mesh orientation. Example problems incorporating enrichment functions for mode II kinematics are also presented. The results yield acceptable crack paths compared with experimental studies. The applicability of the enrichment functions to problems with anisotropy, large strains, and inelasticity is the subject of ongoing studies. Preliminary results for a contrived orthotropic elastic material reflect a decrease in accuracy with increased orthotropy but do not preclude their application to this class of problems.
- Research Organization:
- Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1011660
- Report Number(s):
- SAND2010-2771C; TRN: US201109%%564
- Resource Relation:
- Conference: Proposed for presentation at the Presentation to Students and Faculty at New Mexico Tech held April 27, 2010 in Socorro, NM.
- Country of Publication:
- United States
- Language:
- English
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