Analytical expressions for odd-order anisotropic tensor dimension

International audienceAccording to the symmetries of the matter the number of coe cients needed to de ne a tensorial relation varies. Itis well-known that in linear elasticity the number of generic coe cients 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 coe cients 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 imension of any anisotropic system for third-order piezoelectricity tensors and of the fth-order coupling tensors of Mindlin's strain-gradient elasticity are determined