Modeling of both tensional-shear and compressive-shear fractures by a unified phase-field model

Abstract

Many phase-field models have been developed in recent years to captue different fracture modes from tensional to shear, tensional-shear, and compressive-shear fractures. However, there seems no phase-field model that can simulate the tensional, shear, tensional-shear, and compressive-shear fractures at the same time under complex stress states. In this paper, a unified phase-field model is proposed in the framework of the original phase-field theory. A universal fracture criterion, that can predict both tensional-shear and compressive-shear fractures under complex stress states is embedded in the proposed phase-field, and the failure compression strength is introduced to consider the fracture under a compressive stress state. Therefore, the crack direction can be directly determined from the universal fracture criterion. The strain energy of undamaged configuration is decomposed into three parts, the tensional/compressive part, the shear part, and the rest part. The tensional/compressive and shear parts can be degraded by different degradation functions or the same degradation function. Cohesive fracture models with general softening laws and the classical brittle fracture model can be used in the proposed model, and the length scale has much less influence on the global response if cohesive fracture models with general softening laws are applied. Numerical examples show that the proposed model has the ability to simulate both the tensional-shear and compressive-shear fractures in rock-like materials and the results are in good agreement with the experiments.