A non-Gaussian theory for rubber in biaxial strain. I. Mechanical properties

The theory makes use of the inverse Langevin expression for the force-extension relation for the single chain of n randomly-jointed links. An affine deformatiom of chain vector lengths is assumed on subjection of the network to pure homogeneous strain. The equations for the principal stresses are solved by numerical computation, using the Gauss quadrature method for evaluation of the relevant integrals. Numerical data are given for the whole range of principal extension ratios in biaxial strain for n = 25 and 100, and also for the particular case of simple extension for n = 16, 25, 36, 64 and 100. The results account in a semi-quantitative manner for an important feature of experimental biaxial-strain data which has only recently been observed, and which is not accounted for by previous network theories.