abstract
- The work addresses quantitative characterization of cracks of certain class of ¿irregular¿ (non-elliptical) geometries. This responds to needs of applications where cracks typically have non-circular shapes. The present work focuses specifically on 3D flat cracks of narrow shapes in isotropic materials. Their contributions to the effective elastic properties are analyzed; the cross-property connection implies similar results for the effective conductive properties. A method of estimation of compliance contributions of cracks of narrow shapes is based on treating a crack as a set of 2D plane strain cross-sections. It is shown that the plane strain approximation is quite accurate for sufficiently elongated cracks, as tested on rectangular, elliptical, and curved shapes. For shorter shapes, the stiffening effect of the crack ends becomes noticeable and this effect is estimated; its incorporation into the plane strain framework provides an almost perfect accuracy. In particular, explicit expressions are given for the compliance contributions of the rectangular and annular crack geometries.