https://cea.hal.science/cea-02042420Masson, RenaudRenaudMassonEDF R&D MMC - MatÃ©riaux et MÃ©canique des Composants - EDF R&D - EDF R&D - EDF - EDFNew explicit expressions of the Hill polarization tensor for general anisotropic elastic solidsHAL CCSD2008Eshelby problemAnisotropic elasticityHill's polarization tensorInclusion[CHIM.ANAL] Chemical Sciences/Analytical chemistry[CHIM.MATE] Chemical Sciences/Material chemistry[PHYS.NEXP] Physics [physics]/Nuclear Experiment [nucl-ex][SHS.GESTION] Humanities and Social Sciences/Business administration[SPI.ACOU] Engineering Sciences [physics]/Acoustics [physics.class-ph]PROVITINA, Olivier2019-02-20 13:51:062019-08-13 01:14:122019-02-20 14:25:01enJournal articleshttps://cea.hal.science/cea-02042420/document10.1016/j.ijsolstr.2007.08.035application/pdf1Except for particular cases, the classical expressions of the Eshelby or Hill polarization tensors, depend, respectively, on a simple or double integral for a fully anisotropic two-dimensional or three-dimensional elastic body. When the body is two-dimensional, we take advantage of Cauchy's theory of residues to derive a new explicit expression which depends on the two pairs of complex conjugate roots of a quartic equation. If the body exhibits orthotropic symmetry, these roots are explicitly given as a function of the independent components of the elasticity tensor. Similarly, the double integral is reduced to a simple one when the body is three-dimensional. The corresponding integrand depends on the three pairs of complex conjugate roots of a sextic equation which reduces to a cubic one for orthotropic symmetry. This new expression improves significantly the computation times when the degree of anisotropy is high. For both two and three-dimensional bodies, degenerate cases are also studied to yield valid expressions in any events.