Geodesic
Calculation of the stress-strain state in a pre-loaded elastoplastic body with the sequential formation of cavities based on the theory of repeated superposition of large deformations
Čebyševskij sbornik, Tome 25 (2024) no. 4, pp. 239-249 Cet article a éte moissonné depuis la source Math-Net.Ru

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A numerical solution to the problem of the stress-strain state in a body made of an elastoplastic material with the sequential formation of several cavities in it after preliminary loading at finite deformations has been obtained and studied. To model plasticity, the Mises condition and the law of plastic flow associated with this condition were used. A general mechanical formulation of the problem is given based on the theory of repeated superposition of large deformations. The general solution algorithm is outlined. To solve the problem, we used the finite element method and its modification — the spectral element method. The solution was obtained using methods and algorithms of the engineering strength analysis system. Some results of numerical calculations are presented for the plane static problem of stress concentration in the vicinity of three elliptical cavities formed in a body of square cross-section in the case of plane strain. Effects caused by plasticity, geometric nonlinearity, and redistribution of finite deformations were studied. The results were compared for cases of sequential and simultaneous formation of cavities.
Keywords: elastoplastic material, repeated superposition of large deformations, finite element method, spectral element method, stress concentration near cavities. 
@article{CHEB_2024_25_4_a15,
     author = {V. A. Levin and K. M. Zingerman and M. A. Kartsev and K. A. Petrovskiy},
     title = {Calculation of the stress-strain state in a pre-loaded elastoplastic body with the sequential formation of cavities based on the theory of repeated superposition of large deformations},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {239--249},
     year = {2024},
     volume = {25},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2024_25_4_a15/}
}
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V. A. Levin; K. M. Zingerman; M. A. Kartsev; K. A. Petrovskiy. Calculation of the stress-strain state in a pre-loaded elastoplastic body with the sequential formation of cavities based on the theory of repeated superposition of large deformations. Čebyševskij sbornik, Tome 25 (2024) no. 4, pp. 239-249. http://geodesic.mathdoc.fr/item/CHEB_2024_25_4_a15/