On the derivative of some tensor-valued functions

Padovani C

Materials  Mechanics of Materials  Mechanical Engineering  General Materials Science  Physical science and engineering 

An explicit expression of the derivative of the square root of a tensor is provided, by using the expressions of the derivatives of the eigenvalues and eigenvectors of a symmetric tensor. Starting from this result, the derivatives of the right and left stretch tensor U, V and of the rotation R with respect to the deformation gradient F, are calculated. Expressions for the material time derivatives of U, V and R are also given.

Source: JOURNAL OF ELASTICITY, vol. 58 (issue 3), pp. 257-268

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