{"title":"位错对具有静水压力的非线性弹性圆柱管平衡稳定性的影响","authors":"Evgeniya V. Goloveshkina, Leonid M. Zubov","doi":"10.1007/s00161-023-01255-3","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 1","pages":"27 - 40"},"PeriodicalIF":1.9000,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Influence of dislocations on equilibrium stability of nonlinearly elastic cylindrical tube with hydrostatic pressure\",\"authors\":\"Evgeniya V. Goloveshkina, Leonid M. Zubov\",\"doi\":\"10.1007/s00161-023-01255-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":525,\"journal\":{\"name\":\"Continuum Mechanics and Thermodynamics\",\"volume\":\"36 1\",\"pages\":\"27 - 40\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2023-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Continuum Mechanics and Thermodynamics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00161-023-01255-3\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Continuum Mechanics and Thermodynamics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00161-023-01255-3","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MECHANICS","Score":null,"Total":0}
Influence of dislocations on equilibrium stability of nonlinearly elastic cylindrical tube with hydrostatic pressure
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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This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena.
Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.
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