A Multilevel Adaptive Mesh Scheme for Efficient Simulation of Thermomechanical Phase-Field Fracture

The numerical modeling of thermomechanical fracture is an essential aspect of designing critical components in various industries, including aerospace, automobile, and nuclear. The phase-field method is a suitable approach for simulating thermomechanical fracture problems. However, this method can be computationally expensive. In this study, we propose a multilevel adaptive mesh refinement (ML-AMR) using a phase-field approach, for thermomechanical fracture problems. The proposed approach can efficiently and accurately capture the crack topology without the need for any pre-refinement or explicit marking of damage boundary. Our proposed ML-AMR algorithm introduces an error estimator based on effective crack driving energy computed based on thermomechanical loading using the three prominently used phase-field models (AT2, AT1, and PF-CZM). We demonstrate the accuracy and computational efficiency of the proposed method by simulating various thermomechanical fracture problems and comparing the results with the nonadaptive phase-field method that adopts a priori nonadaptively refined meshes. We consider different types of thermal and mechanical loading, including thermal shock, to evaluate the proposed approach comprehensively. Our results show that the proposed ML-AMR phase-field method reduces computation time by 78%–99% while accurately capturing the crack path, peak load, and total strain energy.