Numerical homogenization of elastic properties and plastic yield stress of rock-like materials with voids and inclusions at same scale

Mechanical properties of rock-like materials are affected by voids and mineral inclusions. Different kinds of analytical solutions have been established for the determination of effective elastic properties and plastic yield stress or failure strength of those materials. However, voids and inclusions are generally considered at different scales. By adopting the Fast Fourier Transform technique, we propose in this paper a numerical homogenization method for modeling the effective elastic properties and plastic yield stress of rock-like materials having voids and mineral inclusions at the same scale. Both are embedded in an elastic-perfectly plastic matrix. The overall elastic-plastic properties are estimated by taking into account the morphology and spatial distribution of pores and inclusions. It is found that the macroscopic elastic modulus is sensitive to both void and inclusion geometry and orientation. The overall yield stress is mainly controlled by the porosity, the inclusion volumetric fraction, the void shape, distribution and orientation. Due to the presence of voids, the influences of inclusion geometry and orientation on the overall yield stress are significantly reduced. This is an important difference with inclusion-reinforced materials without voids.