A peridynamics formulation for quasi-static fracture and contact in rock

We present a dual-horizon peridynamics (DH-PD) formulation for fracture in granular and rock-like materials. In contrast to discrete crack methods such as XFEM, DH-PD does not require any representation of the crack surface and criteria to treat complex fracture patterns such as crack branching and coalescence. The crack path is the natural outcome of the simulation. In this manuscript, a new penalty method to model the contact for compressive fractures and constraining the penetration conditions is developed. The new method is applied to several benchmark problems in geomechanics including the four-point shear test, the indirect tensile (Brazilian) test of rock disks with one or multiple initial cracks. By using an appropriate damping coefficient, the quasi-static solution for rock failure is obtained when the dynamic formulation is used. A good agreement is obtained between the results given by DH-PD and those by the experiments.