A micromechanics-based fractional frictional damage model for quasi-brittle rocks

For quasi-brittle rocks, a novel micromechanics-based fractional friction-damage coupling model is presented by combining the fractional plasticity theory and the micromechanical formulations for cracked solids. The plastic deformation is stemmed directly from the frictional sliding along microcracks while the damage is related to the initiation and propagation of microcracks. These two dissipation processes are inherently coupled. By applying the stress-fractional plasticity operation and the covariant transformation technique, a fractional operation instead of plastic potential is proposed to capture the non-orthogonal plastic flow. In addition, an energy release rate based damage criterion is adopted to describe material degradation. For numerical implementation, a novel explicit return mapping (ERM) integration algorithm is put forward. The predictive performance of the model is verified by comparisons with the associated model (fractional order alpha = 1) and laboratory observations from literatures. Moreover, the effectiveness of the ERM algorithm is assessed numerically.