DETERMINATION OF C1/2, C-1/2 AND MORE GENERAL ISOTROPIC TENSOR FUNCTIONS OF C

In the polar decomposition where F is the (invertible) deformation gradient tensor, U and V are, respectively, the (symmetric) right and left stretch tensors, R is an orthogonal tensor and I is the identity tensor, one faces the problem of determining U, V and R in terms of F. U and U** minus **1 are special examples of isotropic tensor functions of C. Using the representation theorem for isotropic tensor functions together with the diagonalization of a symmetric tensor, the author presents an alternate way of determining U, U** minus **1 and other more general isotropic tensor functions in terms of C. Since U and U** minus **1 are very simple functions of C, one can determine them easily without recourse to the representation theorem and the diagonalization. This is shown in this study. The author treats U and U** minus **1 as isotropic tensor functions of C. In doing so, he shows that U and U** minus **1 can be represented by lower powers of C when U has a repeated eigenvalue.