ON TRANSVERSELY ISOTROPIC, ORTHOTROPIC AND RELATIVE ISOTROPIC FUNCTIONS OF SYMMETRICAL TENSORS, SKEW-SYMMETRICAL TENSORS AND VECTORS .5. THE IRREDUCIBILITY OF THE REPRESENTATIONS FOR 3-DIMENSIONAL ORTHOTROPIC FUNCTIONS AND THE SUMMARY

In this part, the irreducibility of the representations derived in Part IV or three dimensional orthotropic scalar-valued, vector-valued, symmetric tensor-valued and skew symmetric tensor-valued functions of symmetric tensors, skew-symmetric tensors and vectors is proved. Finally, a summary for all of this five-part paper is also given.