Dynamic mechanical behavior of filled polymers. II. Applications

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Abstract
A filled-polymer composite theory, based on effective medium theory, has been developed that allows the dynamic mechanical behavior to be modeled. The stress–strain behavior of the composite is derived using Schapery’s nonequilibrium thermodynamic basis for generalizing Boltzmann’s superposition principle, in conjunction with a Prony series representation for the stress relaxation moduli. Schapery’s theory allows nonlinear viscoelastic effects to be included into the mechanical response. The coefficients of the Prony series are functions of the filler’s bulk modulus, concentration, and shape. The theory is applicable to rubbery polymers and is shown to be accurate for filler concentrations up to approximately 30%. Higher concentrations can be modeled by introducing a phenomenological filler–filler correlation parameter. Effects due to heating and varying strain rate are easily accounted for in this approach. To demonstrate the utility and validity of the theory we compare its predictions to several dynamic experiments on filled-polymer composites. A discussion is provided on implementing the theory in three-dimensional finite element simulations.