The rheological behavior of styrene–butadiene rubber (SBR) compounds filled with silica is investigated as a function of silica volume fraction. To predict the mechanical response, a continuum model for entangled polymer melts filled with nanoparticles is herein introduced. This model is capable of describing the rheological response in both the linear and nonlinear viscoelastic regimes in the context of non-equilibrium thermodynamics to guarantee its thermodynamic admissibility. The constitutive model describes the polymer nanocomposite melts at a mesoscopic level of description by considering the conformation tensor between successive entanglement points, and the orientation tensor for the, in general, spheroidal nanoparticles that describes their average orientation. Evolution equations are developed for nanoparticles with an arbitrary shape but are eventually specified to the case of spherical ones. The multimode version of the new constitutive model provides a very accurate prediction of the rheological behavior of the processability range of SBR/silica nanocomposites. Thus, the new model is a tool able to provide answers to the several difficulties that rubber-producing manufacturers face when processing rubber compounds.

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