Asymptotic homogenization of viscoelastic composites with periodic microstructures

systematic way of obtaining the effective viscoelastic moduli in time and frequency domain is presented for viscoelastic composites with periodic microstructures. The problem of estimating the effective moduli is formulated using the asymptotic homogenization method. For theoretical aspects, the memory effects due to the homogenization are shown in general form and a sufficient condition for the effects to disappear is fully discussed. The computational procedure is divided into two steps. The effective relaxation moduli are computed in Laplace transformed domain and are numerically inverse-transformed into time domain. The effective complex moduli are then readily obtained by using simple formulae of the Fourier transform. Several numerical examples are presented to illustrate and verify present approach and to discuss the memory effects. © 1998 Elsevier Science Ltd.