Nonlinear deformation waves in solids and dispersion

In contemporary technology, high-speed loading, high frequencies and high-amplitude excitations are widely used. For proper analysis, the microstructure of solids must then be taken into account. Together with nonlinear effects, the dispersive effects due to the microstructure are of importance. In this paper, the Mindlin-type model based on the theory of continua is used for describing the microstructure. On the other hand, it is shown how straight-forward numerical methods, like the finite-volume methods, permit to describe the material properties for every discrete element used in numerical simulation. Several phenomena like the existence of solitary waves, the emergence of solitary wave trains, and waves in piece-wise nonlinear laminated materials are briefly discussed and further problems indicated.