Table of Contents
ISRN Nanomaterials
Volume 2013, Article ID 981616, 6 pages
Research Article

The 3D Kuramoto-Sivashinsky Equation for Nonequilibrium Defects Interacting through Self-Consisting Strain and Nanostructuring of Solids

Physics Faculty, Lomonosov Moscow State University, Moscow 119991, Russia

Received 25 June 2013; Accepted 2 September 2013

Academic Editors: R. Hong, G. Jin, and A. Pyatenko

Copyright © 2013 V. I. Emel’yanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is shown that the bulk defect-deformational (DD) nanostructuring of isotropic solids can be described by a closed three-dimensional (3D) nonlinear DD equation of the Kuramoto-Sivashinsry (KS) type for the nonequilibrium defect concentration, derived here in the framework of the nonlocal elasticity theory (NET). The solution to the linearized DDKS equation describes the threshold appearance of the periodic self-consistent strain modulation accompanied by the simultaneous formation of defect piles at extremes of the strain. The period and growth rate of DD nanostructure are determined. Based on the obtained results, a novel mechanism of nanostructuring of solids under the severe plastic deformation (SPD), stressing the role of defects generation and selforganization, described by the DDKS, is proposed. Theoretical dependencies of nanograin size on temperature and shear strain reproduce well corresponding critical dependencies obtained in experiments on nanostructuring of metals under the SPD, including the effect of saturation of nanofragmentation. The scaling parameter of the NET is estimated and shown to determine the limiting small grain size.