The constitutive equation for finite deformations of a transversely isotropic hyperelastic material with residual stress
The strain energy \(\widehat{\sigma}\) for a material described in the title is viewed as a scalar-valued function of the right stretch tensor \(U\) and a residual stress tensor \(T^ 0\) which is invariant under the set of all rotations about a single preferred axis. Thus \(\widehat{\sigma}\) can be expressed as a function of 18 basic polynomial invariants of \(U\) and \(T^ 0\). Assuming that such \(\widehat{\sigma}\) is known, the author shows how the Piola-Kirchhoff stress tensor and the Cauchy stress tensor can be computed in terms of \(\partial \widehat{\sigma}/\partial U\).
scientific article; zbMATH DE number 549821