Gauss-Codazzi Equations for Thin Films and Nanotubes Containing Defects

  • Svyatoslav DerezinEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15)


In the present work we develop the theory of linear defects (dislocations and disclinations) in thin films and nanotubes. Particular attention is given to the geometrical side of the theory, namely, to the Gauss-Codazzi equations of strain compatibility (incompatibility) that determine in general the presence in the body of residual or eigen-strains. We obtain equivalent coordinate-free and covariant formulations of these equations. In addition some special cases of anholonomic isometric transformations of a plane into a surface with defects representing quasi-plastic or incoherent bending are considered. An elegant analogy is drawn with the equations describing steady motions of an ideal incompressible fluid with prescribed vorticity.


Gauss-Codazzi equations Dislocations Disclinations Thin films Nanotubes 


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Southern Federal UniversityRostov on DonRussia

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