Some universal solutions for incompressible elastic bodies that are not Green elastic

Abstract

Universal solutions are found for isotropic elastic bodies, for a class of constitutive equation that is not Green elastic, wherein the linearized strain is assumed to be a function of the Cauchy stress. The structure of the solutions is compared with one example from the classical theory of nonlinear elasticity, namely the case of the inflation and uniform extension/compression of a cylindrical annulus.