Coupled microplane and micromechanics model for describing the damage and plasticity evolution of quasi-brittle material

Quasi-brittle materials exhibit significant heterogeneity due to their complex mesoscopic components and microdefects, and their macroscopic mechanical behavior depends strongly on crack initiation, propagation and friction-slip. In this study, by coupling microplane and micromechanics, a new constitutive model that can consider the mesoscopic damage and plasticity mechanisms of quasi-brittle materials is proposed. The microplane is used throughout the whole construction process for the model: first, a representative volume element (RVE) is established to characterize the mesoscopic structure of quasi-brittle materials, and the advantages of microplanes are fully exploited to characterize the equivalent cracks‒matrix system. Then, the relationship between macroscopic and microplane strains (stresses) is elucidated. Second, considering the unilateral effect for cracks, the expressions for the free energy potential functions for a microplane and for the RVE are established. Third, for each microplane, the damage criterion characterized by the damage driving force is constructed for the open and closed cracks, and in particular, a new plasticity criterion characterizing the static friction property coupled damage and dilatancy behavior during strain softening deformation is constructed. By considering the characteristics of the microplane to relate macroscopic and mesoscopic stress and strain, an efficient return mapping algorithm based on the Newton‒Raphson method is derived. Finally, the stress‒strain curves and the evolution of damage and plasticity are simulated under conventional triaxial compression, uniaxial tensile, direct shear and true triaxial compression stress paths, and the effectiveness of the model is verified by comparison to the experimental data. To better reflect the inherent correlation between mesoscopic damage and macroscopic mechanical behavior, a microplane configuration that can visually characterize the mesoscopic evolution characteristics of damage is established, and it is shown that the simulated results correspond well to the macroscopic deformation and failure pattern of granite samples under different loading paths.