Strongly nonlinear theory of nanostructure formation owing to elastic and nonelastic strains in crystalline solids

We develop an essentially nonlinear theory of elastic and nonelastic microstrains resulting in the formation of nanostructures. Using the model of mutually penetrating lattices, we generalize the well-known theory of acoustic and optical vibrations to the case of nonlinear interaction between sublattices. This permits treating the sublattice interaction forces as periodic (for example, sinusoidal) functions of the relative displacement of the sublattices. We obtain equations for the macroscopic and microscopic displacement fields containing two characteristic scales of the nanostructure. We find a number of their solutions describing the effects of decrease in the potential interatomic barriers in the external stress field and the formation of defects and domain nanostructure as a result of bifurcation transitions. We prove their stability.