ON TRANSVERSELY ISOTROPIC, ORTHOTROPIC AND RELATIVE ISOTROPIC FUNCTIONS OF SYMMETRICAL TENSORS, SKEW-SYMMETRICAL TENSORS AND VECTORS .2. THE REPRESENTATIONS FOR 3-DIMENSIONAL TRANSVERSELY ISOTROPIC FUNCTIONS

There are five kinds of transversely isotropic groups which define the symmetry properties of three dimensional materials which are referred to as being transversely isotropic. In this part, we derive the complete representations for three dimensional transversely isotropic scalar-valued, vector-valued, symmetric tensor-valued and skew-symmetric tensor-valued functions of symmetric tensors, skew-symmetric tensors and vectors. The irreducibility of the representations is proved in Part III.