The systematic nature of regularization error in phase field modeling: implications for crack nucleation and propagation

A critical issue in simulating the evolution of a crack using the phase field approach resides in the ability of the model to predict crack nucleation. In this work, we study the impact of the Ambrosio–Tortorelli regularized crack formulation on the phase field model’s ability to represent the phenomena of nucleation and early crack propagation in two-dimensional domains under generic boundary conditions. Through numerical experiments we study the nature of the errors introduced by the crack’s regularization at the early stages of crack propagation and its critical effects on the predictability of the nucleation phenomenon. We also show that the errors introduced through the regularization of the crack are systematic and can be predicted for a broad range of boundary conditions. Both external and internal crack cases are analyzed and the scalability of the error is verified. We then investigate the nature of the error and identify its localization with reference to the crack geometry. We conclude that the classical formulation of phase field is not designed to predict nucleation without affecting the early propagation of the crack.