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

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


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.


Nonlinear Theory Macroscopic Strain Complex Lattice Relative Shear Mutual Displacement 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

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

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