Phase-field model for 2D cohesive-frictional shear fracture: An energetic formulation

This paper presents a phase-field model for cohesive-frictional shear fracture. The model is derived based on two energetic principles: the energy conservation law and a variational inequality of virtual work that serves as a stability condition. We show that all the governing equations for frictional fracture can be obtained from the above two principles, including the equilibrium condition, the phase-field evolution law and, most importantly, the yield function and flow rule for the plasticity-like frictional slip. The information of crack direction is naturally included in the flow rule. Theoretical and numerical results show that the proposed model is faithfully consistent with the Mohr–Coulomb theory of frictional failure in terms of the crack nucleation stress and direction. In addition, the presented phase-field model has an explicit frictional cohesive law.