Rotation Invariance for Spatial Dispersion Property of the Elastic Constants
In this paper, invariance under rotation for the first-order and second-order spatial dispersion properties of the elastic constants was researched based on group theory. Softwares for calculating and judging invariance under arbitrary rotation of various order spatial dispersion tensors of the elastic constants were programmed by means of Mat lab. With the help of the softwares which we programmed, the general forms of the first-order and second-order spatial dispersion tensors of the elastic constants which belong to the group SO (2) were got, and it is judged that the above tensors of crystals or quasicrystals which have some degree axis of rotation had invariance under arbitrary rotation about the corresponding axes of rotation. The results were of importance to theoretical and experimental research for higher order spatial dispersion effects of the elastic constants.
H. L. Wang and Y. H. Liu, "Rotation Invariance for Spatial Dispersion Property of the Elastic Constants", Applied Mechanics and Materials, Vols. 110-116, pp. 3322-3326, 2012