Effective behavior of long and short fiber-reinforced viscoelastic composites

We study the homogenized properties of linear viscoelastic composite materials in three dimensions. The compos-ites are assumed to be constituted by a non-aging, isotropic viscoelastic matrix reinforced by square or hexagonal arrangements of elastic transversely isotropic long and short fibers, the latter being cylindrical inclusions. The effective properties of these kind of materials are obtained by means of a semi-analytical approach combining the Asymptotic Homogenization Method (AHM) with numerical computations performed by Finite Elements (FE) simulations. We consider the elastic-viscoelastic correspondence principle and we derive the associated local and homogenized problems, and the effective coefficients in the Laplace-Carson domain. The effective coefficients are computed from the microscale local problems, which are equipped with appropriate interface loads arising from the discontinuities of the material properties between the constituents, for different fibers' orientations in the time domain by inverting the Laplace-Carson transform. We compare our results with those given by the Lo-cally Exact Homogenization Theory (LEHT), and with experimental measurements for long fibers. In doing this, we take into consideration Burger's and power-law viscoelastic models. Additionally, we present our findings for short fiber reinforced composites which demonstrates the potential of our fully three dimensional approach.