A three-dimensional micromechanics model for the damage of brittle materials based on the growth and unilateral effect of elliptic microcracks

Based on the analysis of a representative elliptic microcrack embedded in a RVE, the additional compliance tensor induced by an embedded opening/closed microcrack is derived, and that corresponding to the kinked growth of a closed elliptic microcrack is also derived by making use of its approximately equivalent simplification. The effect of the microcracks is analyzed with the Taylor’s scheme by introducing an appropriate probability density function. A three-dimensional micromechanics damage model is obtained for brittle materials, assuming numerous randomly distributed elliptic microcracks and taking into account their deformation, frictional sliding, growth and kinked growth.