For nonlinearly elastic micropolar media, a condition of the existence of weak discontinuous solutions of equations of motion has been obtained. For these solutions, which constitute acceleration waves, the continuity of the second derivatives of displacement and microrotation fields is broken on certain singular surfaces. In the framework of the micropolar-medium model (Cosserat continuum), each particle has the degrees of freedom of an absolutely rigid body, their rotation interaction may be taken into account, and couple stresses exist in addition to standard stresses. The Cosserat model is used to describe granulated, powder-like, and loose media, as well as polycrystalline bodies, composites, and nanostructures. It is also applied to develop non-classical models of thin-walled constructions: bars, plates, and shells.
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