Uniaxial compressive failure of brittle materials as instability of damaging microcracked solids

Uniaxial compressive failure of brittle materials is modelled as buckling of microcracked solids undergoing damage. The brittle material is modelled as an isotropic linear elastic matrix containing a random distribution of non-interacting microcracks. Increasing the stress level, the material response evolves from isotropy at the natural state to orthotropy in damaged states. Furthermore, the overall stiffness decreases until a critical condition of equilibrium bifurcation may be reached. The related critical value of the compressive stress, provided by the buckling analysis of orthotropic elastic sheets, is then assumed as compressive strength of the brittle material. In order to predict damage evolution and model the incremental response, simplified crack configurations are considered. The obtained theoretical results show the dependence of the compressive strength on the matrix toughness and microcrack parameters, and are in good correlation with the experimental results obtained on compressed specimens constrained between frictionless devices.