Crack branching and merging simulations with the shifted fracture method

We propose a relatively simple and mesh-independent approach to model crack branching and merging using the Shifted Fracture Method (SFM), within the class of Shifted Boundary Methods. The proposed method achieves mesh independency by accurately accounting for the area of the fracture surface, in contrast to traditional element-deletion/node-release techniques. In the SFM, the true fracture is embedded into the computational grid, but the fracture interface conditions are modified (shifted) by means of Taylor expansions to the surrogate fracture composed of full edges/faces in two/three dimensions. This avoids numerical integration on cut elements, so that the data structures and geometrical treatment of cut elements are simple, while mesh-independent results and accurate fracture approximations are still maintained. We demonstrate the capabilities of the proposed approach in a number of prototypical numerical experiments.