Damage and Fracture Mechanics Approaches to Mixed-Mode Discrete Fracture with Dilatancy

In this manuscript mixed-mode fracture in quasi-brittle materials is studied. A damage model is first introduced in the framework of the discrete crack approach, in which the limit surface is defined in the traction space. Dilatancy is included in this model as an additional compliance. Some experimental results are simulated, which give rise to further refinement of the model due to the effect of dilatancy. One new model is introduced, based on a nonlinear fracture mechanics approach. This is a purely incremental hypoelastic model, which cannot be derived in the framework of the damage mechanics theory. The numerical results of the two models are compared. In particular, it is found that the fracture mechanics model can better meet the requirements needed for the simulation of the experimental results.