# On Statistical Micromechanical Theories for Brittle Solids with Interacting Microcracks

## Abstract

The nonlinear mechanical responses of damaged solids due to the existence, growth, and nucleation of microdefects are of significant importance to engineers, and have been the subject of many investigations. See Krajcinovic (1989) for a literature review on damage mechanics. For brittle materials, in particular, microcracks often control overall deformation and failure mechanisms. To date, the only exact results derived for microcrack-weakened brittle solids are for dilute microcrack concentrations, where microcrack interactions are entirely neglected. These micromechanical damage models are called “Taylor’s models”. On the other hand, several approximate micromechanical analyses (“effective medium methods”) were proposed in the literature to account for interaction effects of distributed microcracks.

## Keywords

Representative Volume Element Probability Density Function Compliance Matrix Brittle Solid Microcrack Density## Preview

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