균질화법에 의한 점탄성 재료의 유효 물성치 추정

Abstract

A systematic way of obtaining the effective viscoelastic moduli in time and frequency domain is developed for viscoelastic composites with periodic microstructures. The problem of estimating the effective moduli is formulated using the asymptotic homogenization method. The memory effects due to the homogenization is shown in general form and a sufficient condition for the effects to disappear is discussed. The effective relaxation moduli are computed in Laplace transform domain and are numerically inverse-transformed into time domain. The least-square fitting in Laplace transform domain is employed based on the Prony series representations of the relaxation moduli. The effective complex moduli are obtained by using simple formulae of the Fourier transform. Several numerical examples are presented to illustrate and verify present approach, to compare the calculated effective moduli with those of other approaches and to discuss the memory effects. The effect f number of fitting terms on the effective moduli is shown. It is also shown that maximum damping can be obtained by designing specific configuration of the microstructures of the composites.