Molecular chain networks and strain energy functions in rubber elasticity

A relatively simple molecular-statistical model for rubber elasticity, similar to the Wang-Guth and the Arruda-Boyce (AB) models, is presented. Discussion of some approximate inverse Langevin functions leads to the selection of a new one as the most attractive balance between accuracy and simplicity. Use of this approximation with the AB model, in particular, yields the logarithmic strain energy introduced by Gent that exhibits limiting chain extensibility. A rather unusual facet of the relationship between the three strain energies is that the new one is the mean of the other two. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.