Characterization of Elasticity-Tensor Symmetries Using SU(2)

A symmetry class of an elasticity tensor, c, is determined by the variance of this tensor with respect to a subgroup of the special orthogonal group, SO(3). Using the double covering of SO(3) by the special unitary group, SU(2), we determine the subgroups of SU(2) that correspond to each of the eight symmetry classes. A family of maps between C² and R³ that preserve the action of the two groups is constructed. Using one of these maps and three associated polynomials, we derive new methods for characterizing the symmetry classes of elasticity tensors. Mathematics Subject Classifications (2000) 74B05, 74E10.