3D extension of Tensorial Polar Decomposition. Application to (photo-)elasticity tensors

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• 作者：Rodrigue Desmorat^a ; ^{desmorat@lmt.ens-cachan.fr" class="auth_mail" title="E-mail the corresponding author} ; Boris Desmorat^b ; ^c
• 关键词：Harmonic decomposition ; Anisotropy ; Elasticity ; Elasto-optics ; Rari-constant tensor ; Feldspar ; Taurine
• 刊名：Comptes Rendus Mécanique
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：344
• 期：6
• 页码：402-417
• 全文大小：455 K

文摘

The orthogonalized harmonic decomposition of symmetric fourth-order tensors (i.e. having major and minor indicial symmetries, such as elasticity tensors) is completed by a representation of harmonic fourth-order tensors H$\mathbb{H}$ by means of two second-order harmonic (symmetric deviatoric) tensors only. A similar decomposition is obtained for non-symmetric tensors (i.e. having minor indicial symmetry only, such as photo-elasticity tensors or elasto-plasticity tangent operators) introducing a fourth-order major antisymmetric traceless tensor Z$\mathbb{Z}$. The tensor Z$\mathbb{Z}$ is represented by means of one harmonic second-order tensor and one antisymmetric second-order tensor only. Representations of totally symmetric (rari-constant), symmetric and major antisymmetric fourth-order tensors are simple particular cases of the proposed general representation. Closed-form expressions for tensor decomposition are given in the monoclinic case. Practical applications to elasticity and photo-elasticity monoclinic tensors are finally presented.