A consistent phase field model for brittle fracture with new crack driving force

Abstract

Phase field model has been widely used in fracture due to its excellent properties, but diverse simulation results are obtained from different phase field models. To address the variability of the results of different models, a consistent phase field model for brittle fracture is constructed in this paper. Firstly, by re-expressing the evolution equation of the phase field model, it is found that the differences between different models mainly come from the crack driving force. Therefore, a new crack driving force is presented in this paper, and a similar phase field model evolution equation is established to make a closer connection between the AT1 and AT2 models. Subsequently, the effect of phase field gradient is analyzed theoretically. When there is no gradient effect, the new AT1 and AT2 models have the same damage evolution characteristics; when there is a gradient influence, they also have good consistency and reduce the inter-model variability. Finally, some numerical examples are used to study the mechanical properties of the AT1 and AT2 models in the absence and presence of phase field gradient. The results indicate that the two models have similar damage evolution properties, verifying the validity of the models.