Some results for generalized neo-Hookean elastic materials

Several deformations of non-linear elastic materials are used to study the implications of the strain energy density function being dependent only on the first strain invariant. Two kinds of results are obtained, those that compare responses with and without dependence on the second invariant, and those specific to materials whose strain energy functions depend only on the first strain invariant. The deformations are (i) homogenous biaxial extension, (ii) shear superposed on triaxial extension, (iii) inflation of a circular membrane, (iv) circular shear superimposed on a press fit cylinder, (v) torsion of a circular cylinder.