Compliance and Hill polarization tensor of a crack in an anisotropic matrix

摘要: This work aims at developing an efficient method to compute the compliance due a crack modeled as flat ellipsoid of any shape in infinite elastic matrix arbitrary anisotropy (Eshelby problem) when no closed-form solution seems currently available. Whereas this problem usually requires calculation so-called fourth-order Hill polarization tensor if is not singular, it shown that can be derived from first-order term Taylor expansion with respect smallest aspect ratio ellipsoidal inclusion. For 3D model, expressed simple integral thanks Cauchy residue theorem. A similar allows express same case cylindrical model without integral. numerical example finally treated.