A review of characteristic lengths in the coupled criterion framework and advanced fracture models - Molnár, Gergely; Doitrand, Aurélien; Estevez, Rafael; Gravouil, Anthony (Comptes Rendus. Mécanique)
The review paper explores the significance of characteristic lengths in fracture mechanics, focusing on the Coupled Criterion framework. It addresses limitations in traditional Linear Elastic Fracture Mechanics, which struggle to predict small-scale crack behaviors, and highlights the need for models that allow characteristic lengths to emerge from material properties and geometry rather than being predefined inputs.The review covers two main characteristic lengths: the initiation crack length and Irwin’s length, examining their interactions with lengths used in other fracture approaches such as Phase-Field methods, Cohesive Zone Models, and atomic-scale simulations. The findings show that Irwin’s length consistently appears in models that combine stress and energy criteria, indicating its fundamental role in fracture prediction.The study identifies limitations in current models, especially in cases involving strong singularities or where the energy condition dominates, and suggests improvements by incorporating process zone descriptions or regularization techniques from Phase-Field models. These enhancements could better capture the complex behaviors at smaller scales.The paper concludes by advocating for a combined approach that integrates various fracture models, which could provide a more comprehensive understanding of crack initiation and propagation across different scales. This integrative strategy would allow for more accurate predictions and a deeper insight into the mechanics of fracture.