Summary
A parametric nonlinear model of two-dimensional textile metamaterials is formulated to investigate the free undamped propagation of elastic waves. The mechanical system is characterized by spatially periodic prestressed configuration and governed by differential difference equations with quadratic and cubic nonlinearities arising from the elastic contact between plain woven wires. By combining Fourier transforms and multiple scale methods, the linear dispersion properties of the metamaterial are described, and their weakly nonlinear perturbations are asymptotically determined as analytical function of the wave oscillation amplitude.
