Thermo-mechanical modeling of a filled elastomer based on the physics of mobility reduction

•A new physical nonlinear thermoviscoelastic approach is proposed to understand and to model the influence of stiff micro- or nanometre-sized filler particles on the mechanical material behavior.•The glass transition temperature of the matrix material which is constant in the original Williams-Landel-Ferry equation is replaced by a nonlinear function dependent on a modified von mises invariant of the stress tensor and its distance(s) to the filler surface(s).•The single non-linear viscoelasticity without yield stress replicates the state of confinement as well as the coupling between temperature dependence and stress softening. The payne effect, a specific application of the law has been studied. The addition of rigid fillers to an elastomeric matrix enhances its mechanical properties. This reinforcement effect is primarily due to a filler network structure in which polymer regions between aggregates play the principal role. In this study, a continuum constitutive equation is formulated for polymer behavior under strong confinement conditions. This behavior can be accounted for by a local glass transition temperature that combines the effects of physical interaction and stress softening in a unique viscoelastic formulation. The model reproduces, at a microscopic scale, the processes governing the Payne effect, including the temperature dependence of the viscoelastic behavior of the filled elastomer reinforcement.