The generalized curie principle, the hermann theorem, and the symmetry of macroscopic tensor properties of composites

Abstract

The symmetry of tensor properties of composite materials is discussed in terms of the generalized Curie principle (including the effect of symmetrizing factors), as well as the Hermann theorem concerning the relationship between the rank of a tensor property and the presence or absence of isotropy in a plane normal to a given symmetry axis. A simple configuration for achieving this transverse isotropy for the elastic behaviour of laminated structures is proposed as an illustration of the practical application of the Hermann theorem. A recently published theorem about the point symmetry of composite objects is shown to be invalid.