Simple determination of stretch and rotation tensors, more general isotropic tensor-valued functions of deformation

Using the representation theorem, interpolation methods for isotropic tensor-valued functions and the extended Cayley-Hamilton theorem, we present a way of determining U, U^-1, V, V^-1, R (without recourse to eigenvectors) in terms of C, B and F, respectively. We consider other more general isotropic tensor-valued functions of C and B (ln U, for example). We obtain some simple to calculate and new formulas for these functions in 2-dimensional and 3-dimensional cases of deformation.