Adaptive PF-CZM for multiphysics fracture analysis in functionally graded materials

Functionally graded materials (FGM) hold significant relevance in engineering due to their tailored material property gradation, designed for specific engineering applications. The challenge in fracture analysis of FGM stems from the spatial variation of material properties, which complicates the prediction of crack topology. Local and global refinement strategies are impractical for fracture analysis in FGM due to the unpredictable nature of crack topology, which renders local refinement infeasible. Additionally, global refinement is not advisable as it leads to a significant increase in degrees of freedom, adversely affecting computational efficiency.

The novelty of this research lies in the incorporation of spatial variation in both the length scale and material properties, enhancing the realism of FGM domain modeling. To preserve the required length scale, it is necessary to adopt a minimum mesh size, which consequently results in a substantial increase in the degrees of freedom and, thereby, escalates the computational cost. To address these challenges, the study employs an adaptive mesh refinement (AMR) algorithm integrated with a phase-field cohesive zone model (PF-CZM), providing a robust solution for accurate fracture analysis in FGM. Based on the ideas stemming from the need for efficient and realistic modeling, the AMR-PF-CZM framework refines the mesh efficiently in regions of crack growth based on crack-driving energy and phase field variable, thereby eliminating the need for pre-refinement. The findings demonstrate a 76%–85% increase in computational efficiency and accuracy of the AMR-PF-CZM approach compared to the non-adaptive PF-CZM. Furthermore, the developed algorithm’s applicability to dynamic fracture and multi-physics problems, specifically addressing mechanical and thermal fracture in FGM, underscores the importance of this approach in capturing complex fracture phenomena.