Analysis of nonlinear wave propagation in hyperelastic network materials

We analyze the acoustic properties of microstructured repetitive network material undergoing configuration changes leading to geometrical nonlinearities. The effective constitutive law of the homogenized network is evaluated successively as an effective first nonlinear 1D continuum, based on a strain driven incremental scheme written over the reference unit cell, taking into account the changes of the lattice geometry. The dynamical equations of motion are next written, leading to specific dispersion relations. The inviscid Burgers equation is obtained as a specific wave propagation equation for the first order effective continuum when the expression of the energy includes third order contributions, whereas a perturbation method is used to solve the dynamical properties for the effective medium including fourth order terms. This methodology is applied to analyze wave propagation within different microstructures, including the regular and reentrant hexagons, and plain weave textile pattern.