Viscoelastic Homogenization Approach for Damping Properties of Polymer Composites Using Fractional Calculus

Polymer composites are attractive material system with damping ability to reduce vibration of mechanical structures and improve controllability of mechanical system. To understand effect of constituents and microstructure on damping properties of polymer composites, a detailed micromechanical study is needed to develop the method of analysis for microscopic viscoelastic deformation and macroscopic damping properties. Viscoelastic homogenization approach with fractional calculus is developed to evaluate effective damping properties of polymer composites. The microstructure of the composite is supposed to be periodic and polymer matrix is viscoelastic medium. Damping properties of the composite are evaluated from the stress strain diagram and associated energy dissipation during cyclic loading. Viscoelastic properties of the polymer matrix are identified using a generalized fractional Maxwell model with spring and fractional elements. Coefficients of elements in the generalized fractional Maxwell model are determined to be fitting into experimental data in frequency domain. The homogenized stress strain relation in time domain given by inverse Laplace transform is derived and numerical calculations are carried out.