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

We consider deformations and motions that correspond to a non-uniformaxial stretch superimposed to a general pseudoplane deformationof the first kind. We provide the general determining equationfor this kind of solution when the constitutive equation forthe stress tensor is derived from the elastic neo-Hookean strain-energydensity. Then we provide some explicit solutions which are generalizationsof the non-symmetric torsion of a slab and some finite-amplitudepseudo-planar elliptical motions.