Phase field modeling of crack propagation in structures under tensile stress

This paper presents a numerical implementation of phase field models in structures subjected to tensile stress in both quasi-static and dynamic fracture cases. It focuses on the AT1 model and the phase field regularized cohesive zone model (PF-CZM) to compare their performance. Within these models, we focus on implementing the irreversibility condition using the penalization method rather than (Miehe et al. in Comput Methods Appl Mech Eng 199(45–48):2765–2778, 2010. https://​doi.​org/​10.​1016/​j.​cma.​2010.​04.​011)’s “History field” method. Moreover, we employed a staggered algorithmic implementation due to its proven robustness. Numerical simulations were conducted using the multi-physic finite element code, COMSOL Multiphysics. The geometries analyzed include a notched and un-notched confined beam under stretching load and a ring under internal pressure. The originality of this work is presented in two parts. The first part consists in the implementation of the penalization technique within COMSOL Multiphysics. Then we investigated the effects of parameters like cohesive softening laws, notch depth and shape, mesh sensitivity, and length scale sensitivity on the confined beam responses. The second part of this manuscript consists in studying the dynamic fragmentation of a ring under internal pressure. A new solution is proposed to capture crack nucleation and propagation without randomizing material parameters.