Nonlinear wave propagation analysis in hyperelastic 1D microstructured materials constructed by homogenization

We analyze the acoustic properties of microstructured beams including a repetitive network material undergoing configuration changes leading to geometrical nonlinearities. The effective constitutive law is evaluated successively as an effective first and second order nonlinear grade 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 presence of second gradient order term in the nonlinear equation of motion leads to the presence of two different modes: an evanescent subsonic mode for high nonlinearity that vanishes beyond certain values of wave number, and a supersonic mode for a weak nonlinearity. This methodology is applied to analyze wave propagation within different microstructures, including the regular and reentrant hexagons, and plain weave textile pattern.