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 man ifests itself as a reduction of moduli and/or change in elastic consta nts. This paper presents the effective elastic moduli of a solid conta ining inclusions and a general distribution of tunnel cracks. Both in- plane and out-of-plane elastic constants are determined. In addition t o crack density and inclusion volume fraction, the effective elastic c onstants are found to depend on a function rho(theta), which character izes the crack orientation distribution, while the anisotropy of a cra cked composite is solely induced by the crack orientation distribution . It is established that the effect of inclusions and microcracks on e ffective moduli is decoupled, i.e., one can obtain the moduli of a sol id containing microcracks and inclusions by the corresponding moduli o f the solids with microcracks only and with inclusions only. For a sol id containing a crack distribution with mirror symmetry, the effective elastic constants can be greatly simplified and can be expressed in t erms of two scalar quantities rather than a general function rho(theta ). This conclusion is particularly useful in the analysis of the micro mechanical model. The effect of the asymmetry of rho(theta) on the eff ective elastic constants is also investigated.