Self-consistent micromechanical approach for damage accommodation in rock-like polycrystalline materials

In quasi-brittle polycrystalline materials, damage by cracking or cleavage dominates plastic and viscous deformation. This paper proposes a micromechanical model for rock-like materials, incorporating the elastic-damage accommodation of the material matrix, and presents an original method to solve the system of implicit equations involved in the formulation. A self-consistent micromechanical approach is used to predict the anisotropic behavior of a polycrystal in which grain inclusions undergo intragranular damage. Crack propagation along planes of weakness with various orientation distributions at the mineral scale is modeled by a softening damage law and results in mechanical anisotropy at the macroscopic scale. One original aspect of the formulated inclusion–matrix model is the use of an explicit expression of Hill’s tensor to account for matrix ellipsoidal anisotropy. To illustrate the model capabilities, a uniaxial compression test was simulated for a variety of polycrystals made of two types of mineral inclusions with each containing only one plane of weakness. Damage always occurred in only one mineral type: the damaging mineral was that with a smaller shear modulus (respectively higher bulk modulus) when bulk modulus (respectively shear modulus) was the same. For two minerals with the same shear moduli but different bulk moduli, the maximum damage in the polycrystal under a given load was obtained at equal mineral fractions. However, for two minerals with different shear moduli, the macroscopic damage was not always maximum when the volume fraction of two minerals was the same. When the weakness planes’ orientations in the damaging mineral laid within a narrow interval close to the loading direction, the macroscopic damage behavior was more brittle than when the orientations were distributed over a wider interval. Parametric studies show that upon proper calibration, the proposed model can be extended to understand and predict the micro–macro behavior of different types of quasi-brittle materials.