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Article Dans Une Revue Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Année : 2011

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

Résumé

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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Dates et versions

hal-00687817 , version 1 (15-04-2012)

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  • HAL Id : hal-00687817 , version 1

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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 A: Mathematical, Physical and Engineering Sciences, 2011, 467 (2126), pp.314-332. ⟨hal-00687817⟩
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