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Influence of dislocations on equilibrium stability of nonlinearly elastic cylindrical tube with hydrostatic pressure

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Abstract

The phenomenon of buckling of a nonlinearly elastic hollow circular cylinder with dislocations under the action of hydrostatic pressure is studied. The tensor field of the density of continuously distributed dislocations is assumed to be axisymmetric. The subcritical state is described by a system of nonlinear ordinary differential equations. To search for equilibrium positions that differ little from the subcritical state, the bifurcation method is used. Within the framework of the model of a compressible semi-linear (harmonic) material, the critical pressure at which the loss of stability occurs is determined, and the buckling modes are investigated. The effect of edge dislocations on the equilibrium bifurcation is analyzed. It is shown that the loss of stability can also occur in the absence of an external load, i.e., due to internal stresses caused by dislocations.

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Acknowledgements

The reported study was funded by the Russian Science Foundation, Project Number 23-21-00123, https://rscf.ru/en/project/23-21-00123/.

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  1. Institute of Mathematics, Mechanics, and Computer Science, Southern Federal University, 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.V., Zubov, L.M. Influence of dislocations on equilibrium stability of nonlinearly elastic cylindrical tube with hydrostatic pressure. Continuum Mech. Thermodyn. 36, 27–40 (2024). https://doi.org/10.1007/s00161-023-01255-3

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