An implicit adaptive finite volume-based phase-field model for dynamic fracture

Abstract

A novel and efficient adaptive finite volume-based phase-field framework is proposed for simulating dynamic fracture in brittle and quasi-brittle solids using implicit time integration schemes. The method builds upon the variational phase-field theory of fracture and is formulated within the finite volume method (FVM), yielding conservative, symmetric, and diagonally dominant discrete systems. To enhance computational efficiency, adaptive mesh refinement (AMR) is incorporated, leveraging the cell-centered FVM’s capability to handle hanging nodes and mesh irregularities without additional constraints. The framework incorporates both the AT2 and phase-field cohesive zone models to enhance versatility. To rigorously assess the accuracy, robustness, and efficiency of the proposed framework, a systematic parametric study is first conducted on a dynamic crack branching benchmark, examining the model’s sensitivity to various factors, including time integration schemes, mesh resolution, cell topology, and initial defect morphology. The effectiveness and accuracy of AMR are also assessed under varying tensile loading conditions. Additionally, benchmark examples such as dynamic shear loading, dynamic fragmentation of a thick cylinder, and fracture of a concrete compact tension specimen are simulated. Finally, the method is applied to a challenging 3D multiple-fracture problem, demonstrating its ability to capture complex spatial crack interactions, encompassing branching and coalescence. All results show good agreement with existing numerical and experimental data, confirming the accuracy, mesh insensitivity, and predictive capability of the proposed framework for dynamic fracture simulation.