The simple shifted fracture method

We propose a simplified version of the Shifted Fracture Method (SFM), which relies on an approximate fracture geometry representation combined with approximate interface conditions. In particular, we show that the complexities of earlier SFM implementations, associated with the use of a mixed variational formulation of the equilibrium equations, can be avoided. This approach has minimal impact on the overall accuracy of numerical computations but leads to considerable gains in performance. These outcomes can be justified because the proposed simplified SFM accurately accounts for the area of the fracture surface and prevents the severe mesh dependencies observed in classical cohesive zone models or node-release/element-deletion techniques. We also show that the proposed approach can be combined with a phase-field model to more easily capture branching and merging of fractures.