A Simple and Robust Mesh Refinement Implementation in Abaqus for Phase Field Modelling of Brittle Fracture

The phase field model can coherently address the relatively complex fracture phenomenon, such as crack nucleation, branching, deflection, etc. The model has been extensively implemented in the finite element package Abaqus to solve brittle fracture problems in recent studies. However, accurate numerical analysis typically requires fine meshes to model the evolving crack path effectively. A broad region must be discretized without prior knowledge of the crack path, further augmenting the computational expenses. In this proposed work, we present an automated framework utilizing a posteriori error-indicator (MISESERI) to demarcate and sufficiently refine the mesh along the anticipated crack path. This eliminates the need for manual mesh refinement based on previous experimental/computational results or heuristic judgment. The proposed Python-based framework integrates the pre-analysis, sufficient mesh refinement, and subsequent phase-field model-based numerical analysis with user-defined subroutines in a single streamlined pass. The novelty of the proposed work lies in integrating Abaqus’s native error estimation and mesh refinement capability, tailored explicitly for phase-field simulations. The proposed methodology aims to reduce the computational resource requirement, thereby enhancing the efficiency of the phase-field simulations while preserving the solution accuracy, making the framework particularly advantageous for complex fracture problems where the computational/experimental results are limited or unavailable. Several benchmark numerical problems are solved to showcase the effectiveness and accuracy of the proposed approach. The numerical examples present the proposed approach’s efficacy in the case of a complex mixed-mode fracture problem. The results show significant reductions in computational resources compared to traditional phase-field methods, which is promising.