Essentially nonlinear theory of microdeformations in medium with periodic structure

Abstract

Essentially nonlinear theory of micro and macro deformations of a medium with cardinally rearranging periodic structure is presented using a new model of double continuum with variable local topology. In a frame of proposed model there are two deformation modes (macroscopic and microscopic) when some threshold is reached. Some problems such as twin transitions, catastrophic deformation waves, shock and tilting bifurcation waves are considered. An exact solution describing elasto plastic fragmentation of medium is constructed also when double periodic domain superstructure are formed. There are solid rotons of opposite signs with singular defects between them. They appear in a critical field of macroscopic deformations of pure shear. When this bifurcation point is overcome then dimensions of domains are stabilized. The letter depend on value of macroscopic deformations. Some criterion of global stability is established. .