Catastrophic Microdeformations in Crystalline Lattice. Structure Stability and Modifications

Essentially nonlinear theory of three-dimensional lattice subjected to the intensive shear is presented. Two, acoustic and pseudo optical, branches of deformations are considered. The deformation energy is shown to consist of periodic and gradient terms. The equilibrium equation in the sine-Helmholtz form is exactly solved. It demonstrates some effects of bifurcations. The first effect is the transformation of homogeneous macrodeformation into inhomogeneous one, in which case a superstructure with large periods and a new translation order are formed. The second bifurcation effect is associated with occurrence of two deformed, elastic and elastoplastic, states, in which case the short-range atomic order is altered and a new modification of crystalline lattice is formed. Some criteria of local and global structural stability are revealed.