Rock-like fracture simulation by a double energy-limiter nonlocal damage model

Fracture mechanisms of brittle rocks are usually different from each other, i.e., in mode-I and mode-II. To simulate crack propagation in rock-like materials under compression, the distinctions of mode-I and mode-II failure behavior must be taken into account. Here we present a novel double-nonlocal damage formulation, which is highly suitable for modeling mixed-mode brittle failure in rock and rock-like materials. The damage formulations describe the fracture mechanisms of the two modes through two separate damage evolution equations (corresponding to mode-I and mode-II, respectively) based on our recently developed energy limiter-based gradient-enhanced damage model. The differences in the opening and shear modes of the crack are distinguished by the input data required for the two damage evolution equations including the fracture energy, initial damage thresholds, and crack driving forces. Numerical simulations under the standard FEM framework are performed to reveal the advantages and capacity of the developed double damage model for quasi-static crack growth in rocks. Obtained numerical solutions are then validated to referred experimental data and numerical results from other modeling techniques in the literature to see the accuracy of the developed theory.