Tensors which characterize anisotropies

Abstract

The theory of tensor function representations constitutes a rational basis for a consistent mathematical modelling of complex mechanical behaviour of anisotropic materials. The so-called structural tensors, which characterize the symmetry group of anisotropy of concern, play a key role in obtaining irreducible and coordinate-free representations for anisotropic tensor functions. In this paper, based on available properties of Kronecker products of orthogonal transformations, a simple method of determining the structural tensors with respect to any given symmetry group is developed. As its application, the structural tensors corresponding to the five transverse isotropy groups, all of their finite subgroups, and the symmetry group of the 32 crystal classes, which present the most usual and worthwhile anisotropic symmetry groups, are constructed. In particular, we also show that each of these anisotropic symmetry groups can be characterized by only one simple structural tensor.