Analytical expressions for odd-order anisotropic tensor dimension

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• 作者：Nicolas Auffray p>Nicolas.auffray@univ-mlv.fr" class="auth_mailp>
• 关键词：Anisotropic materials ; Tensors ; Generalized elasticity
• 刊名：Comptes Rendus Mecanique
• 出版年：May 2014
• 年：2014
• 卷：342
• 期：5
• 页码：284-291
• 全文大小：242 K

文摘

According to the symmetries of the matter, the number of coefficients needed to define a tensorial relation varies. It is well known that in linear elasticity the number of generic coefficients varies from 21, for a complete anisotropic material, to 2, in case of isotropy. In a previous contribution, we provided analytical expressions that give the number of generic anisotropic coefficients in any anisotropic system for an even-order tensor. In the present note, we aim at extending the previous results to the case of odd-order tensors. As an illustration, the dimension of any anisotropic system for third-order piezoelectricity tensors and of the fifth-order coupling tensors of Mindlin's strain-gradient elasticity are determined.