A Langevin-elasticity-theory-based constitutive equation for rubberlike networks and its comparison with biaxial stress–strain data. Part I

A structure-based constitutive equation for rubberlike networks is proposed. It is obtained by combining the Langevin-statistics-based theory of Arruda and Boyce (AB) with a term based on the first invariant of the generalized deformation tensor which follows from some theoretical treatments of the constraint effect. The combined (ABGI) four-parameter strain–energy function has been found to give (with the exception of the very-low strain region) a very good description (deviations<5–8%) of a representative selection of published biaxial stress–strain data obtained on networks of isoprene and natural rubbers at low and medium strains. For the description of biaxial extension data up to high strains, the concept of a strain-induced increase in the network mesh size (strain-dependent finite extensibility parameter) used previously for tensile strains, is shown to apply generally to all deformation modes. It also enables a prediction of the retraction behavior. Reasonable values were obtained for the network parameters; the exponent in the strain invariant assumes values at the higher limit of the Kaliske and Heinrich extended tube theory prediction or even somewhat outside the limits.