Nonlinear strain wave localization in periodic composites

Nonlinear strain wave propagation along the lamina of a periodic two-component composite was studied. A nonlinear model was developed to describe the strain dynamics. The model asymptotically satisfies the boundary conditions between the lamina, in contrast to previously developed models. Our model reduces an initial two-dimensional problem into a single one-dimensional nonlinear governing equation for longitudinal strains in the form of the Boussinesq equation. The width of the lamina may control the propagation of either compression or tensile localized strain waves, independent of the elastic constants of the materials of the composite.