Analytical expressions for odd-order anisotropic tensor dimension

作者：Auffray Nicolas^*

来源：Comptes Rendus Mecanique, 2014, 342(5): 284-291.

DOI：10.1016/j.crme.2014.01.012

• Anisotropic materials
• Tensors
• Generalized elasticity

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.

• 出版日期2014-5