Analytic stress-strain relationship for isotropic network model of rubber elasticity

James and Guth [3] have used the inverse Langevin function-based expression of tension in a polymer chain to build the so-called 3-chain model of unco mpressible rubber elasticity. It is an analytical model, but it is not isot ropic. if one considers an isotropic superposition of an infinite number of chains in all the directions, one obtains an isotropic model, but it is no more tractable analytically. Following Cohen [12], we propose to replace t he inverse Langevin function by its Pade approximant, the two functions bei ng very close. The isotropic model is then analytically integrable, and yie lds large strain strain-stress relationship. (C) 2000 Academic des sciences /Editions scientifiques et medicales Elsevier SAS.