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Shell-like Structures pp 531–548Cite as

Gauss-Codazzi Equations for Thin Films and Nanotubes Containing Defects

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Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 15))

Abstract

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.

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Authors and Affiliations

  1. Southern Federal University, Milchakova str. 8a, 344090, Rostov on Don, Russia

    Svyatoslav Derezin

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  1. Svyatoslav Derezin
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Correspondence to Svyatoslav Derezin .

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Editors and Affiliations

  1. Magdeburg, Institut für Mechanik, Otto-von-Guericke-Universität, Universitätsplatz 2, Magdeburg, 30106, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Halle-Wittenberg, Martin-Luther-Universität, Kurt-Mothes-Str. 1, Halle, 06120, Germany

    Victor A. Eremeyev

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Derezin, S. (2011). Gauss-Codazzi Equations for Thin Films and Nanotubes Containing Defects. In: Altenbach, H., Eremeyev, V. (eds) Shell-like Structures. Advanced Structured Materials, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21855-2_35

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