On anisotropic functions of vectors and second order tensors - all subgroups of the transverse isotropy group C_∞h

Abstract

A unified procedure for constructing both the generating sets and the functional bases is suggested, which reduces the representation problem for anisotropic functions of any finite number of vector and second order tensor variables under any subgroup g ⊂ C_∞h, to that for the same types of anisotropic functions of not more than two vector and/or second order tensor variables. By using this procedure and new results for isotropic extension of anisotropic functions, simple irreducible generating sets and functional bases in unified forms are presented to determine general reduced forms of scalar-, vector-, and second order tensor-valued anisotropic functions of any finite number of vectors and second order tensors, under all kinds of subgroups of the transverse isotropy group C_∞h. The results given are derived in the sense of nonpolynotnial representation.