On transversely isotropic, orthotropic and relative isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Part IV: The representations for three dimensional orthotropic functions

Abstract

The three groups which define the symmetry properties of the three crystal classes in the rhombic system are referred to as being three dimensional orthotropic. In the present part the complete representations for three-dimensional orthotropic scalar-valued, vector-valued, symmetric tensor-valued and skew-symmetric tensor-valued functions of symmetric tensors, skew-symmetric tensors and vectors are determined. The irreducibility of these representations is proved in the final part V of this paper. In addition, a generalization for these representations is given.