A unified enrichment scheme for fracture problems

An enrichment scheme is presented in the framework of the extended finite element method (XFEM) that is independent of the material model. In the case of linear elastic fracture mechanics (LEFM), i.e. brittle fracture, stresses are singular at the crack-tip, whereas, in the case of cohesive fracture models, i.e. quasi-brittle cracks, stresses are finite at the crack-tip. Despite of the stress situation at the crack-tip, stresses are always finite in the region near the crack-tip and have a high gradient in the near-tip region. In order to cover almost all the stress gradients near the crack-tip, an optimal set of enrichment functions is found that can interpolate all the near-tip stress gradients starting from a large gradient that can no longer be captured by a standard FEM up to the situation where the gradient is almost infinite. An optimization study is conducted in order to find the optimal set of enrichment functions with respect to some error criterion. Test cases for static and quasi-static cracks are presented to show the usefulness and robustness of the proposed technique. In the case of brittle fracture, better results are achieved as compared to those obtained by the classical branch enrichments. The enrichment scheme is also used for the case of cohesive fracture and excellent agreement to available benchmarks is achieved.