Reconstruct lower-dimensional crack paths from phase-field point cloud

Because of the smeared representation of phase-field fracture, reconstructing lower-dimensional crack paths is challenging, which may impede the further applications of the phase-field method in the modeling of fault friction and fluid flow in fracture. In the present work, we propose to capture the crack curves or surfaces from two-dimensional or three-dimensional phase-field point cloud using an optimized ridge regression algorithm, and k-nearest neighbor and principal component analysis are used to estimate the normal direction of each segment on the identified discrete crack path. The sensitivity and computational efficiency of the proposed method are investigated thoroughly. Subsequently, this method is extended to reconstruct the complex discrete fracture networks. Finally, several benchmarks for fracture, fault friction and fluid flow problems are presented to demonstrate the strength of the proposed approach.