An efficient adaptive multi-mesh phase-field method for simulating rock fractures

Abstract

Phase-field models have significant advantages in rock fractures, such as simulating multiple crack initiation, propagation and coalescence without requiring fracture criteria. However, the high computational cost is a notable drawback. For this reason, this paper proposes a simple, efficient and robust Adaptive Multi-Mesh phase-field method (AMM) for modelling crack propagation. The main concept of the AMM method is to adopt a coarser adaptive mesh and C0 elements for the displacement field in order to reduce computational cost, while employing a finer adaptive mesh and C1 elements for the damage field to accurately capture in-rock crack paths. The results show that the AMM method is capable of reducing the number of displacement elements by 58.2–72% and the computational time by 43.8–53% compared to the Adaptive Mesh phase-field method (AM), and by 92.4–96.4% and 95.9–98.8%, respectively, compared to the Uniform Refinement mesh method (UR). Additionally, this paper also proposes a simple and practical mesh Refinement Combination Strategy, RCS, and an efficient Local variable transfer method, LEI, which requires only the Exchange of Integration point positions. The proposed RCS makes it possible to perform variable transfer between two independent adaptive meshes without searching the topological relations, thus dramatically decreasing the implementation difficulty and computational time. The proposed LEI method achieves variable transfer simply by exchanging integration point positions, thereby ensuring simplicity and numerical stability.