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.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Aero, E.L.: Structural transitions and shear stability of polyatomic layers. Inorg. Mater. 35(8), 860–862 (1999)
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)
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)
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)
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
Born, M., Huang, K.: Dynamic Theory of Crystal Lattices. Clarendon Press, Oxford (1954)
Cosserat, E., Cosserat, F.: Théorie des corps déformables. Hermann, Paris (1909)
Kosevich, A.M.: Theory of Crystal Lattice. Vyshcha Shkola, Kharkov (1988). In Russian
Kunin, I.A.: Elastic Media with Microstructure. II Three-Dimensional Models. Springer, Berlin (1983)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Aero, E.L., Bulygin, A.N. (2010). Nonlinear Theory of Cardinal Rearrangement of the Solid Body Structure in the Field of Intensive Pressure. In: Maugin, G., Metrikine, A. (eds) Mechanics of Generalized Continua. Advances in Mechanics and Mathematics, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5695-8_13
Download citation
DOI: https://doi.org/10.1007/978-1-4419-5695-8_13
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-5694-1
Online ISBN: 978-1-4419-5695-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)