Definitions
Volterra dislocation is a special state of an elastic multiply connected body in which the strain tensor and the free energy density are single-valued and continuous in the domain occupied by the body, and displacements and rotations possess multivalence of a certain type. Generally, the Volterra dislocation consists of a translational dislocation which is characterized by the Burgers vector and a disclination, defect of rotational type, which is characterized by the Frank vector.
Introduction
Defects like dislocations and disclinations play an important role in the mechanical behavior of different slender structures, e.g., plates, shells, two-dimensional crystals, carbon nanotubes, etc.
The mathematical theory of dislocations appeared for the first time in the work of Volterra (1907). He analyzed the behavior of linear elasticity solutions in multiply connected domains. The main principles of the nonlinear theory...
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References
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Zubov, L., Derezin, S. (2018). Elastic Shells, Dislocations, and Disclinations. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_198-1
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DOI: https://doi.org/10.1007/978-3-662-53605-6_198-1
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