3D numerical manifold method for crack propagation in rock materials using a local tracking algorithm

The modeling of crack growth in three-dimensional (3D) space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock materials. In this study, we present a novel approach that introduces a 3D numerical manifold method (3D-NMM) with a geometric kernel to enhance computational efficiency. Specifically, the maximum tensile stress criterion is adopted as a crack growth criterion to achieve strong discontinuous crack growth, and a local crack tracking algorithm and an angle correction technique are incorporated to address minor limitations of the algorithm in a 3D model. The implementation of the program is carried out in Python, using object-oriented programming in two independent modules: a calculation module and a crack module. Furthermore, we propose feasible improvements to enhance the performance of the algorithm. Finally, we demonstrate the feasibility and effectiveness of the enhanced algorithm in the 3D-NMM using four numerical examples. This study establishes the potential of the 3D-NMM, combined with the local tracking algorithm, for accurately modeling 3D crack propagation in brittle rock materials.