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

Abstract

A structure-based constitutive equation for rubberlike networks (ABGIL) was proposed in Part I of this communication. It is a combination of the connectivity term based on Langevin statistics (Arruda and Boyce, AB) and a constraint term which follows from some theoretical treatments and may be expressed in the form of the first invariant of the generalized deformation tensor (GI). The ABGIL equation was tested in Part I using published biaxial stress–strain data on networks of natural and isoprene rubbers and further tests are performed in Part II on networks of poly (dimethylsiloxane) and styrene–butadiene rubber. Parameters of the equation were obtained from the fitting procedure. Apart from the region of very low (<10%) strains, a good, or even very good description (less than 5% deviation) of the experimental biaxial stress–strain behavior was obtained. In the region of very high strains, the previously introduced concept of a strain-dependent finite-extensibility parameter was applied. The effects of polymer and network structure and presence of a diluent in the course of endlinking on the fitted parameter values are discussed. The values of the exponent n in the constraint term were found to lie in a rather wide range (−0.2 to +1) which includes predictions of four different tube theories.