Derivatives of the stretch and rotation tensors (Q1330748)

This short paper presents a derivation of explicit expressions for the derivatives of the stretch and rotation tensors with respect to the deformation gradient. These expressions may be useful in the study of some classes of constitutive behavior where one needs to express the stretch and rotation in terms of the deformation gradient. This operation usually involves irrational operations (e.g. taking square roots of tensors) that are awkward. The approach considered uses the very definition of derivatives, so that restrictions of the desired derivatives to subspaces associated with tangent spaces of the stretch and rotation tensors are found.