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Equilibrium stability of nonlinear elastic sphere with distributed dislocations

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Abstract

An exact formulation and a solution of the stability problem for a three-dimensional elastic body containing distributed dislocations are given. The buckling phenomenon for a hollow nonlinear elastic sphere of the semi-linear (harmonic) material with edge dislocations is studied. The study is carried out within the framework of the continuum theory of continuously distributed dislocations using the bifurcation method of buckling analysis. The bifurcation method is to find the equilibrium positions of an elastic body, which differ little from the subcritical (unperturbed) state. The perturbed equilibrium state is described by a linearized boundary value problem. By solving a homogeneous linear boundary value problem, the minimum critical value of the external pressure at which the sphere loses stability is found. The influence of dislocations on the buckling of both thin and thick spherical shells is analyzed.

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Acknowledgements

The reported study was funded by the Russian Foundation of Basic Research, Project Number 19-31-90045.

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  1. Institute of Mathematics, Mechanics, and Computer Science, Southern Federal University, Milchakova Str. 8a, Rostov-on-Don, Russian Federation, 344090

    Evgeniya V. Goloveshkina & Leonid M. Zubov

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  1. Evgeniya V. Goloveshkina
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  2. Leonid M. Zubov
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Correspondence to Evgeniya V. Goloveshkina.

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Goloveshkina, E., Zubov, L.M. Equilibrium stability of nonlinear elastic sphere with distributed dislocations. Continuum Mech. Thermodyn. 32, 1713–1725 (2020). https://doi.org/10.1007/s00161-020-00876-2

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