Inversion of higher order isotropic tensors with minor symmetries and solution of higher order heterogeneity problems

Abstract : In this paper, the derivation of irreducible bases for a class of isotropic 2nth-order tensors having particular "minor symmetries" is presented. The methodology used for obtaining these bases consists in extending the concept of deviatoric and spherical parts, commonly used for 2nd-order tensors, to the case of a nth-order tensor. It is shown that those bases are useful for effecting the classical tensorial operations and specially the inversion of a 2nth-order tensor. Finally, the formalism introduced in this study is applied for obtaining the closed form expression of the strain field within a spherical inclusion embedded in an infinite elastic matrix and subjected to linear or quadratic polynomial remote strain fields.
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Vincent Monchiet, Guy Bonnet. Inversion of higher order isotropic tensors with minor symmetries and solution of higher order heterogeneity problems. Proceedings of the Royal Society of London A, 2011, 467 (2126), pp.314-332. ⟨hal-00687817⟩

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