Advertisement

Nonlinear Theory of Cardinal Rearrangement of the Solid Body Structure in the Field of Intensive Pressure

  • Eron L. Aero
  • A. N. Bulygin
Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 21)

Abstract

A nonlinear theory of microscopic and macroscopic strains is developed for the case of large inhomogeneous relative displacements of two sublattices making up a complex crystal lattice. The standard linear theory of acoustic and optical oscillations of a complex lattice is generalized, taking into account new additive principle of internal translational symmetry—relative shear of two sublattices leaving deformation energy invariant. As a result, the force interaction between the sublattices is characterized by a nonlinear periodic force of its mutual displacements. The theory describes large microdisplacements due to bifurcation transitions of atoms into neighboring cells. As a result, the theory predicts defect formations, switching interatomic bonds, phase transitions, formation of nanoclasters, etc. Some examples of resolutions of nonlinear equations of equilibrium are presented.

Keywords

Nonlinear Theory Macroscopic Strain Complex Lattice Relative Shear Mutual Displacement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aero, E.L.: Structural transitions and shear stability of polyatomic layers. Inorg. Mater. 35(8), 860–862 (1999) Google Scholar
  2. 2.
    Aero, E.L.: Micromechanics of a double continuum in a model of a medium with variable periodic structure. J. Eng. Math. 55, 81–95 (2002) CrossRefMathSciNetGoogle Scholar
  3. 3.
    Aero, E.L.: Inhomogeneous microscopic shear strains in a complex crystal lattice subjected to larger macroscopic strains (exact solutions). Phys. Solid State 45(8), 1557–1565 (2003) CrossRefGoogle Scholar
  4. 4.
    Aero, E.L., Bulygin, A.N.: Strongly nonlinear theory of nanostructure formation owing to elastic and nonelastic strains in crystalline solids. Mech. Solids 42, 807–822 (2007) CrossRefGoogle Scholar
  5. 5.
    Aero, E.L., Bulygin, A.N.: Nonlinear theory of localized waves in complex crystalline lattices as discrete-continuum systems. Vichislit. Mech. Sploshn. Sred 1, 14–30 (2008). In Russian Google Scholar
  6. 6.
    Born, M., Huang, K.: Dynamic Theory of Crystal Lattices. Clarendon Press, Oxford (1954) Google Scholar
  7. 7.
    Cosserat, E., Cosserat, F.: Théorie des corps déformables. Hermann, Paris (1909) Google Scholar
  8. 8.
    Kosevich, A.M.: Theory of Crystal Lattice. Vyshcha Shkola, Kharkov (1988). In Russian Google Scholar
  9. 9.
    Kunin, I.A.: Elastic Media with Microstructure. II Three-Dimensional Models. Springer, Berlin (1983) MATHGoogle Scholar
  10. 10.
    Porubov, A.V., Aero, E.L., Maugin, G.A.: Two approaches to study essentially nonlinear and dispersive properties of the internal structure of materials. Phys. Rev. E. 79, 046608 (2009) CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute of Problems in Mechanical EngineeringSt. PetersburgRussia

Personalised recommendations