ELASTIC-MODULI OF HETEROGENEOUS SOLIDS WITH ELLIPSOIDAL INCLUSIONS AND ELLIPTIC CRACKS

The influence of ellipsoidal inclusions and elliptic cracks on the ove rall effective moduli of a two-phase composite and of a cracked body, respectively, is investigated by means of Mori-Tanaka's theory for thr ee types of inclusion and four types of crack arrangements: monotonica lly aligned, 2-D randomly oriented (two kinds for cracks), and 3-D ran domly oriented. The effective moduli of the composite in the aligned c ase are known to coincide with Willis' orthotropic lower (or upper) bo unds with a two-point ellipsoidal correlation function if the matrix i s the softer (or harder) phase. With 2-D randomly oriented inclusions, the effective moduli are examined under Willis' transversely isotropi c bounds with a two-point spheroidal correlation function, and it is f ound that, as the cross-sectional aspect ratio of the ellipsoidal incl usions flattens from circular shape to disc-shape, the two effective s hear moduli and the plane-strain bulk modulus all lie on or within the bounds. The effective bulk and shear moduli of an isotropic composite containing randomly oriented ellipsoidal inclusions also fall on or w ithin Hashin-Shtrikman's bounds as the shape of the ellipsoids changes . The obtained moduli are then extended to a cracked body containing e lliptic cracks, which are generated by compressing the thickness of el lipsoidal voids to zero. It is found that only selected components of the effective moduli are dependent upon the crack density parameter et a. Their dependence on eta and the crack shape gamma are explicitly es tablished.