Numerical modeling of discrete multi-crack growth applied to pattern formation in geological brittle media

We describe a finite element-based method to propagate multiple fractures simultaneously. The algorithm is iterative and it simulates sub-critical quasi-static crack propagation. The matrix is homogeneous and isotropic, and behaves linear elastically. The algorithmic cornerstones are a failure criterion, a propagation criterion, and a propagation angle. Fracture geometries are kept track of independently of the mesh allowing geometric handling of fracture arrest, closure, and coalescence. Fracture aperture is an emergent property of the model. The mesh is adaptively remeshed to capture variations in the geometry and displacement field. Generated patterns reproduce observed crack paths in physical experiments. Algorithm efficiency scales linearly. The model reproduces en-echelon crack linkage, fracture hooking, and orthogonal tip approximation patterns. Our numerical experiments closely match physical experiments. Remeshing consumes <2% of the total computational time demonstrating current computational capabilities allow for discrete crack propagation to be viable for multiple crack propagation.