Constitutive matrices for 32 typical classes of crystalline solids with couple stress, quadrupole, and curvature-based flexoelectric effects (Q6058548)

Two of the major problems for the people which studies higher-order or coupled behavior of anisotropic dielectrics are the derivation and the complete tabular representation for relevant tensorial constitutive quantities. This involves various types of fourth-order and also fifth- and sixth-order tensors. In this paper a neat and clear-cut derivation for various tensorial quantities up to the fourth-order, based on the Neumann principle, is provided. As a truly didactical example, the method is then applied in explicit form for two crystal classes; then in an appendix the data for all the 32 crystal classes are provided. As far as I can remember, the most complete description for the fifth- and sixth-order tensors was provided in a 1953 paper [\textit{R. Fieschi} and \textit{F. G. Fumi}, Nuovo Cimento, IX. Ser. 10, 865--882 (1953; Zbl 0051.22901)] and it would be very interesting to see how the procedure based on the Neumann proposed by the authors could be extended to these higher-order tensors.