The Derivative of Isotropic Tensor Functions, Elastic Moduli and Stress Rate: I. Eigenvalue Formulation
Authors:
- 1 October 2004
- journal article
- research article
- Published by SAGE Publications in Mathematics and Mechanics of Solids
- Vol. 9 (5) , 493-511
Abstract
We derive basis-free formulae for the derivative of general isotropic tensor functions of symmetric tensors, and the formulae for elastic moduli and stress rate for compressible isotropic elastic materials. Part I of this paper concerns the tensor functions with the representation of spectral decomposition. The solution is obtained through the directional derivatives on certain subspaces that span the set of symmetric tensors.Keywords
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