FUNCTIONAL BASES FOR TRANSVERSELY ISOTROPIC AND TRANSVERSELY HEMITROPIC INVARIANTS OF ELASTICITY TENSORS

A set I of 20 invariants for the action of O(2) on the space of elasti city tensors is obtained. It is shown that I, together with seven addi tional invariants linked by seven relations, yield a functional basis for the action of SO(2), while a different set of 21 elements with 21 relations is added to I to form a basis for O(2). These results are ob tained in view of a geometric representation of the group action, irre ducibly decomposed into a direct sum of rotations.