Free wave propagation in pretensioned two-dimensional textile metamaterials

A parametric lattice model is formulated to describe the dispersion properties of harmonic elastic waves propagating in two-dimensional textile metamaterials. Within a weak nonlinear regime, the free undamped motion of the textile metamaterial, starting from a spatially periodic prestressed configuration, is governed by nonlinear differential difference equations, where nonlinearities arise from the elastic contact between plain woven yarns. Within the linear field, the linear dispersion properties characterizing the regime of small oscillation amplitudes are obtained, by applying the Bloch's theorem. Parametric analyses are carried out to study the influence of the mechanical parameters on wavefrequencies, waveforms, and group velocities. As major outcome, the dispersion spectrum is found to possess two distinct passbands, covering the low- and the high-frequency ranges, respectively, while a complete midfrequency bandgap exists for large parameter regions. Within the nonlinear field, the nonlinear wavefrequencies and the multiharmonic nonresonant response in the time domain are described, by means of perturbation techniques. As interesting finding, the free wave is shown to propagate with a systematic softening behavior. The wave polarization exalts the nonlinear effects in the high-frequency passband.