Functional bases for transversely isotropic and transversely hemitropic invariants of elasticity tensors

Abstract

A set I of 20 invariants for the action of O(2) on the space of elasticity tensors is obtained. It is shown that I, together with seven additional 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 obtained in view of a geometric representation of the group action, irreducibly decomposed into a direct sum of rotations.