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In this research, an analytical method is presented for predicting the viscoelastic and dynamic behavior of polymer nanocomposite. The analytical model is achieved by coupling the SUC micromechanical model with standard linear solid model. Boltzmann superposition principle is used to develop the constitutive equations. First, the strain associated with a relaxation experiment is considered, and then by using the idea of linearity as embodied in the Boltzmann superposition principle, the resulting stress history is predicted. Eventually, the creep function corresponding to the relaxation modulus is obtained and the hysteresis loop for nanocomposite material is represented. Creep response is sinusoidal in time and a function of stress history. Loss and storage modulus and material behavior in Laplace domain are obtained using standard linear solid model and SUC micromechanical model, respectively. Standard linear solid model is achieved by paralleling the Kelvin model with Maxwell model. The model is validated with experimental results. Effects of different interphase thickness, CNT volume fraction and phase angle on hysteresis loop is studied. Obtained results reveal that increasing the CNT volume fraction and phase angle leads to decreasing and increasing the nanocomposite hysteresis loop area, respectively. Also, Interphase thickness contains considerable effects on the nanocomposite dynamic behavior.

Keywords: Micromechanics, Unit cell, Viscoelastic, Hysteresis, Standard linear solid

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