Wave propagation in 3D viscoelastic auxetic and textile materials by homogenized continuum micropolar models

We analyze in this contribution the impact of wave damping on the dispersion features of 3D viscoelastic periodic structures, which are modeled as Kelvin–Voigt viscoelastic beam-lattices. The band diagram structure and damping ratio are computed for different repetitive structures, based on the micropolar viscoelastic response of the effective medium obtained by the homogenization of the initially discrete lattice architecture. The employed methodology is herewith exemplified for the cases of the 3D hexagon structure, which shows negative Poisson’s ratio for reentrant configurations, and the 2D plain weave textile structure. The dispersion relations and damping ratio are obtained by inserting an harmonic plane waves Ansatz into the dynamical equations of motion of the obtained effective viscoelastic anisotropic continuum. The 3D reentrant hexagon is an auxetic metamaterial showing excellent wave absorption capabilities, as reflected by the high incidence of partial band gaps. The textile plain weave structure shows a complete band gap for low frequencies. Comparing the frequency band structure of the effective continuum with that obtained by Floquet–Bloch analysis extended to a 3D context shows that the wave propagation characteristics can be directly obtained from the homogenized continuum at low frequencies.