An evaluation of the Gent and Gent-Gent material models using inflation of a plane membrane

Abstract

The Gent material model is the simplest extension of the neo-Hookean material model that can describe the finite extensibility of the polymeric chains comprising the elastomer network. However, it is known that its fitting to experimental results of uniaxial tension is not satisfactory for moderate values of stretch, and the Gent-Gent model was proposed to remedy this deficiency. In this paper we provide further evidence on the good performance of the Gent-Gent model by using it to study the inflation of a circular plane membrane. For this problem, the deformation near the pole is equibiaxial and the associated nominal tension is a monotonic function of the stretch, but the pressure as a function of the stretch has both a maximum and a minimum. The Gent and Gent-Gent models are first fitted to our own experimental data for the nominal tension, and then used to predict variation of the pressure with respect to the stretch. By comparison with the experimental data, it is shown that the Gent-Gent model gives much better predictions than the Gent model.