A self-consistent mechanics method for solids containing inclusions and a general distribution of cracks

The damage in a composite material due to a distribution of cracks manifests itself as a reduction of moduli and/or change in elastic constants. This paper presents the effective elastic moduli of a solid containing inclusions and a general distribution of tunnel cracks. Both in-plane and out-of-plane elastic constants are determined. In addition to crack density and inclusion volume fraction, the effective elastic constants are found to depend on a function ρ{variant}(θ), which characterizes the crack orientation distribution, while the anisotropy of a cracked composite is solely induced by the crack orientation distribution. It is established that the effect of inclusions and microcracks on effective moduli is decoupled, i.e., one can obtain the moduli of a solid containing microcracks and inclusions by the corresponding moduli of the solids with microcracks only and with inclusions only. For a solid containing a crack distribution with mirror symmetry, the effective elastic constants can be greatly simplified and can be expressed in terms of two scalar quantities rather than a general function ρ{variant}(θ). This conclusion is particularly useful in the analysis of the micromechanical model. The effect of the asymmetry of ρ{variant}(θ) on the effective elastic constants is also investigated.