Determination of the effective elastic and damping properties of polymer lattice structures

This paper introduces a numerical framework that models the representative volume element (RVE) of lattice structures made of viscoelastic material to investigate the influence of different RVE topologies on their macroscopic elastic behavior and damping capability. Specifically, these properties are obtained through an energy-based homogenization procedure, while the viscoelastic behavior of the bulk material is described using the Bagley–Torvik fractional derivative model, which describes its frequency-dependent response. A comprehensive numerical campaign is carried out on eleven lattice topologies across a wide range of relative densities and excitation frequencies. Results reveal that, for lattice structures made of a single material phase and the void phase, the macroscopic elastic response is essentially governed by the RVE topology and its relative density. Furthermore, the dependence of equivalent elastic properties on the frequency at the macroscopic scale is consistent with that of the bulk material at lower scale. Finally, despite each RVE topology exhibits a certain elastic symmetry, the loss factors matrix at the macroscopic scale does not depend on the RVE topology and is identical to that of the bulk material. Consequently, the macroscopic complex stiffness tensor exhibits the same frequency dependence as the bulk viscoelastic material, enabling homogenization at arbitrary frequencies.