ON TRANSVERSELY ISOTROPIC, ORTHOTROPIC AND RELATIVE ISOTROPIC FUNCTIONS OF SYMMETRICAL TENSORS, SKEW-SYMMETRICAL TENSORS AND VECTORS .4. THE REPRESENTATIONS FOR 3-DIMENSIONAL ORTHOTROPIC FUNCTIONS

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