A Full-Network Rubber Elasticity Model based on Analytical Integration

Source abstract

Full-network rubber elasticity models generally require numerical integration over the unit sphere. In the present paper, a procedure for analytical integration of power series in terms of stretch square is proposed instead. This procedure is applied both to the inverse Langevin function and its rounded Padé approximation. The integrated power series demonstrates fast convergence to the analytical solution so far as it is available or to the numerical one based on a high resolution integration scheme. Good agreement with experimental data on silicone rubber is obtained as well. The integration procedure is also implemented to average the stretch on the basis of a q-root operator. This operator is usually applied in order to introduce a non-affine relation between micro and macro stretches into a network model.