A coated inclusion-based homogenization scheme for viscoelastic composites with interphases

A coated inclusion-based homogenization scheme is developed for three-phase viscoelastic composites in the Laplace-Carson domain. The interphase between inclusion and matrix is considered as a coating in a composite-like inclusion and shows altered viscoelastic behavior compared to the matrix. The strain concentration equations between the viscoelastic inclusion and the viscoelastic coating are derived with two different models: the double inclusion (denoted DI) model, and the reconsidered double inclusion (RDI) model. Then, the homogenization scheme is based on a modified Mori-Tanaka scheme for three-phase viscoelastic composites, which is validated with the exact analytical formulation in the case of spherical composite inclusions and isotropic behaviors for all constituents. The comparison of the proposed coated inclusion-based homogenization scheme based on the RDI model with the exact analytical solution shows a significant improvement compared to the one based on the DI model in the prediction of effective properties for composites with interphases. Finally, considering experimental dynamic mechanical analyses (DMA) in the frequency domain for a carbon-black filled styrene butadiene rubber from the literature, the effective viscoelastic behavior is estimated with a good accuracy in terms of the storage and loss moduli for different volume fractions of composite inclusions.