Dependence of the dynamic properties of Voigt and Reuss composites on the Poisson's ratios and bulk loss factors of the constituent materials

Materials possessing both high stiffness and high damping would be beneficial in many structural applications. Composites that combine a stiff material, which usually has low damping, with a soft and lossy material have been proposed to engender both high dynamic modulus and high loss factor. In this article, we investigate the effective dynamic moduli and loss factors of Reuss and Voigt composites in response to a uniaxial harmonic load. The constituent materials are characterized by multiaxial viscoelastic models in the frequency domain. Using the viscoelastic correspondence principle, we derive formulae for Reuss and Voigt composites of infinite dimensions taking into account Poisson effects. We show that the effective loss factor of a Reuss composite is sensitive to the values of the Poisson's ratio and bulk loss factors of the constituent materials. Finally we simulate, using finite element analysis, the response of cylindrical Reuss composite rods of finite radius to an axial load. We demonstrate that the effective dynamic properties of these rods is highly sensitive to the ratio of the radius to the layer thickness of the composite.