On the strain energy decomposition in phase field brittle fracture: established models and novel cleavage plane-based techniques

Abstract This work offers a detailed examination of the phase field approach for modeling brittle fracture, emphasizing its theoretical foundations, mathematical descriptions, and computational strategies. Central to our discussion is an in-depth analysis of strain energy decomposition methods integral to phase field models. We introduce an innovative technique using a cleavage plane based degradation that has shown promising results under various loading scenarios. We meticulously evaluate each method’s inherent limitations and challenges to highlight their respective advantages and drawbacks across different loading scenarios. This review aims not only to catalog existing knowledge but also to pave the way for future research directions in the application of phase field approach to fracture analysis.