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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2019, Volume 19, Issue 3, Pages 317–325 (Mi isu810)  

Scientific Part
Mechanics

Axisymmetric stress field near a circular cut in a solid with stress state dependent plastic properties

E. V. Lomakin, N. G. Minaev

Lomonosov Moscow State University, 1 Leninskie Gory, Moscow 119991, Russia

Abstract: The paper analyzes the properties of the constitutive relations of the theory of plasticity for a continuum, which plastic properties depend on the type of stress state. The plasticity condition presented in the corresponding generalized form is used, where the parameter of the type of stress state is introduced, which is the ratio of the hydrostatic stress component to the equivalent von Mises stress, named in the literature the stress triaxiality. For a particular type of plasticity condition, an analytical solution of the problem for a solid with a circular hole under plane strain is obtained. The stress distributions corresponding to the obtained solution are compared with the ones for a solid whose plastic properties are invariant to the stress state using the Huber – Mises plasticity condition. The influence of the degree of sensitivity of materials properties to the type of stress state on the stress distributions in plastic areas are studied.

Key words: plasticity theory, plane deformation, Coulomb – More criterion, plane with a circular cut.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00318_а
17-51-52001_МНТ_а
This work was supported by the Russian Foundation for Basic Research (projects No. 17-01-00318, 17-51-52001).


DOI: https://doi.org/10.18500/1816-9791-2019-19-3-317-325

Full text: PDF file (351 kB)

Bibliographic databases:

UDC: 539.3
Received: 19.05.2019
Accepted:16.06.2019

Citation: E. V. Lomakin, N. G. Minaev, “Axisymmetric stress field near a circular cut in a solid with stress state dependent plastic properties”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 19:3 (2019), 317–325

Citation in format AMSBIB
\Bibitem{LomMin19}
\by E.~V.~Lomakin, N.~G.~Minaev
\paper Axisymmetric stress field near a circular cut in a solid with stress state dependent plastic properties
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2019
\vol 19
\issue 3
\pages 317--325
\mathnet{http://mi.mathnet.ru/isu810}
\crossref{https://doi.org/10.18500/1816-9791-2019-19-3-317-325}
\elib{http://elibrary.ru/item.asp?id=39542336}


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  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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