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.