Comparison between the relaxation spectra obtained from homogenization models and finite elements simulation for the same composite

The objective of this work is to determine the relaxation spectrum of spherical particles reinforced viscoelastic and isotropic composites from 3D Finite Elements (FE) simulations of the microstructure. The matrix and the reinforcements are assumed to be incompressible and Maxwellian. The spectra obtained from the FE simulations are compared with those obtained from analytical homogenization models. This paper presents the procedure used for generating the FE models as well as the procedure used for obtaining relaxation spectra meeting the thermodynamics requirements imposed on linear viscoelastic materials. It seems that the relaxation spectrum for the microstructure studied in this paper is composed of a negligible continuous part and a discrete part of higher intensity. In any case, the resulting material does not have a Maxwellian behavior.