Modeling the response of filled elastomers at finite strains by rigid-rod networks (Q1349256)

The authors derive a model of isothermal time-dependent response of particle-reinforced elastomers at finite strains. The main features of the model are: a) at the micro-level, an amorphous rubbery polymer is treated as a network of rigid-rod chains linked at junctions which deform affinely with the bulk material; b) a strand between two junctions is thought of as a sequence of segments bridged by bonds, and is treated as an ensemble of rigid (inextensible) rods connected in sequence and linked by bonds; c) two possible conformations are described: a bond-flexed conformation and extended conformation. In the free state, the number of bonds in flexed and extended conformations and determined by the condition of thermal equilibirum. Under straining, some bonds are transformed from one conformation to another, and the rate of transformation is determined by the law of thermodynamics; d) the mechanical energy of a strand equals the sum of mechanical energies of bonds in the flexed conformation, whereas the mechanical energy of bonds in the extended conformation is neglected. The mechanical energy of a bond in the flexed conformation is, in the linear theory, a quadratic function of local strain; e) constitutive equations and differential equations of evolution of the concentrations of bonds with various conformations are derived from thermodynamics; f) the constitutive equations are determined by four adjustable parameters which are found by fitting experimental data in uniaxial tensile, compressive and cyclic tests. These parameters are influenced, in a plausible way, by the filter content, cross-link density and temperature. Fair agreement is made clear between the observations for several filled and unfilled rubbery polymers. The effects of the straining state, filler content, cross-link density and temperature on the adjustable constants are thoroughly analyzed.