Asymptotic and numerical homogenization methods applied to fibrous viscoelastic composites using Prony’s series

Abstract

The paper focuses on the evaluation of the effective properties of linear viscoelastic composites with a periodic structure, containing long cylindrical fibers of circular cross-section and for two different cell arrangements: square and hexagonal unit cells. For this purpose, we use the two-scale asymptotic homogenization method (AHM) and a numerical homogenization method (NHM). Based on the correspondence principle, the local functions and the relaxation overall properties are obtained in explicit form by the AHM using the Prony series. Additionally, the NHM is established for a three-dimensional representative cell, and the problem is solved under appropriate boundary conditions, by using the Finite Element Method. The numerical results obtained by the AHM and NHM are compared and verified with other theoretical approaches. The comparisons show a good agreement and a benchmark for further experimental and theoretical investigations.