Cosserat continuum model of wave propagation in layered materials

We derive a model for the long wavelength behaviour of a layered material with smooth interfaces within the framework of Cosserat continuum. In such a continuum three types of waves exist: longitudinal, shear and rotational. The wave velocity in this approximation depends on the direction of propagation, but not on the absolute value of the wave vector. Only a longitudinal wave exists in the directions strictly perpendicular and parallel to the layering. This has a profound effect on the fracture propagation caused by an impact action perpendicular to the layering. The impact will be transferred from one layer to the other at the speed of the longitudinal wave. Thus, when the first layer breaks the longitudinal wave will transmit the load to the next one and so forth, without the energy dissipation that would be associated with the propagation of rotational and shear waves.