The significance of pure measures of distortion in nonlinear elasticity with reference to the Poynting problem

Abstract

The objective of this paper is to show the significance of expressing the strain energy function in terms of a scalar pure measure of dilatation and a tensor pure measure of distortion, which were essentially introduced by Flory [1]. It is shown that convenient representations for the strain energies of dilatation and distortion, and the pressure and deviatoric Cauchy stress may be recorded in terms of these deformation measures. After specializing to the case of an isotropic material, specific constitutive equations are proposed and the Poynting problem is considered. It is shown that the Poynting effect (extension of a bar in torsion) is significantly influenced by coupling between dilatational and distortional strain energies, which is caused by the dependence of the shear modulus on dilatation.