Some generalized pseudo-plane deformations for the neo-Hookean material

摘要

We consider deformations and motions that correspond to a non-uniform axial stretch superimposed to a general pseudoplane deformation of the first kind. We provide the general determining equation for this kind of solution when the constitutive equation for the stress tensor is derived from the elastic neo-Hookean strain-energy density. Then we provide some explicit solutions which are generalizations of the non-symmetric torsion of a slab and some finite-amplitude pseudo-planar elliptical motions.