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Invariants of the stretch tensors and their application to finite elasticity theory. (English) Zbl 1047.74007

Summary: The principal invariants of stretch tensors in the polar decomposition of the deformation gradient stand in one-to-one relation to principal invariants of their squares, Cauchy-Green deformation tensors. These relations are used to obtain the derivatives of the first set of invariants with respect to the deformation gradient. The latter generate expressions for the stretch and rotation factors in the polar decomposition as explicit functions of the deformation gradient, and lead to new formulae for stress and elastic moduli of isotropic elastic materials.

MSC:

74B20 Nonlinear elasticity
15A72 Vector and tensor algebra, theory of invariants
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