Overall viscoelastic properties of 2D and two-phase periodic composites constituted of elliptical and rectangular heterogeneities

This paper presents analytical solutions for the effective rheological viscoelastic properties of 2D periodic structures. The solutions, based on Fourier series analysis, are derived first in the Laplace-Carson (LC) space for different inclusion shapes (rectangle or ellipse) and arrangements. The effective results are obtained in the form of rational functions of the LC transform variable. Two inversion methods are used to find the relaxation behavior. The first one is based on the exact inverse of the LC transform while the second approximates the overall behavior by using a Standard Linear Solid model, which yields very simple analytical formulas for the coefficients entering the constitutive equations. Results of the two methods are compared in the case of an application to real materials.