A novel phase-field model for mixed cracks in elastic–plastic materials incorporating unilateral effect and friction sliding

In this work, we shall develop a novel phase-field model for modeling complex cracking processes in rock like materials under various loading paths. Both smooth frictionless and rough frictional cracks are investigated. For smooth cracks, an elastic-damage model is formulated with the unilateral effect on elastic stiffness tensor at the crack opening–closure transition. For rough cracks, an elastic–plastic damage model is developed, also incorporating the unilateral effect. In particular, for closed rough cracks, the damage evolution is explicitly coupled with the frictional sliding along cracks, which results in the macroscopic plastic deformation. The continuity conditions are verified for all energy functions, stress–strain relations and conjugated thermodynamics forces. By incorporating the friction sliding mechanism, the proposed model is able to properly take into account the dependency of mechanical behavior on confining stress of most geological materials under compressive stresses. The efficiency of the novel model is assessed through various cases, including comparisons between numerical results and experimental observations.