A novel implementation of asymptotic homogenization for viscoelastic composites with periodic microstructures

There is a growing demand for methods to estimate the effective viscoelastic response of viscoelastic composites, for their applications in structural vibration and noise control. This paper proposes a novel reformulation and numerical implementation algorithm for the asymptotic homogenization theory for predicting the effective complex moduli of viscoelastic composites in the frequency domain. In the new algorithm, an equivalent harmonic analysis is established and a double-layer elements method is proposed to solve the local problem in the homogenization process. On the basis of the new algorithm, the effective complex moduli can be obtained easily by using commercial software to serve as a black box. Numerous elements and techniques for modeling and analysis available in commercial software can be applied to complicated microstructures without mathematical derivation. The numerical examples presented show the validity of this new implementation algorithm.