Development of a method for assessing the stability of a new type of crack, the conditions of destruction of the medium and decomposability by simple solutions

Authors

  • Babeshko O.M. Kuban State University, Krasnodar, Российская Федерация ORCID 0000-0003-1869-5413
  • Evdokimova O.V. Kuban State University, Krasnodar, Российская Федерация ORCID 0000-0003-1283-3870
  • Babeshko V.A. Kuban State University, Krasnodar, Российская Федерация ORCID 0000-0002-6663-6357
  • Gorshkova E.M. Kuban State University, Krasnodar, Российская Федерация ORCID 0000-0002-2415-6224
  • Evdokimov V.S. Kuban State University, Krasnodar, Российская Федерация
  • Zaretsky A.G. Kuban State University, Krasnodar, Российская Федерация
  • Bushueva O.A. Kuban State University, Krasnodar, Российская Федерация

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-19-4-37-47

Abstract

In the work with the application of the universal modeling method previously developed by the authors, an in-depth analysis of cracks of a new type was carried out. A method for constructing integral equations of a new type has been developed and methods for solving them have been proposed. New features of cracks of a new type are revealed and an approach is described that allows the study of cracks of a new type in environments of complex rheologies. The approach is based on the block element method, decomposability of solutions of complex boundary value problems by solutions of boundary value problems for simpler Helmholtz equations, factorization methods. As a result of the study, the features of the destruction of the medium by cracks of a new type and the nature of the stresses excited by harmonic oscillations of wave fields are revealed. In this paper, using the example of the Lame equations, it is shown how the formed cracks of a new type will be transferred to environments of more complex rheology using solutions for environments of simpler rheologies.

Keywords:

new type cracks, block elements, factorization, integral equations, external forms, Lame equations

Acknowledgement

The work was supported by the Russian Science Foundation (project 22-29-00213).

Author Infos

Olga M. Babeshko

д-р физ.-мат. наук, главный научный сотрудник научно-исследовательского центра прогнозирования и предупреждения геоэкологических и техногенных катастроф Кубанского государственного университета

e-mail: babeshko49@mail.ru

Olga V. Evdokimova

д-р физ.-мат. наук, главный научный сотрудник научно-исследовательской части Кубанского государственного университета

e-mail: evdokimova.olga@mail.ru

Vladimir A. Babeshko

академик РАН, д-р физ.-мат. наук, заведующий кафедрой математического моделирования Кубанского государственного университета

e-mail: babeshko41@mail.ru

Elena M. Gorshkova

канд. физ.-мат. наук, старший научный сотрудник Научно-исследовательского центра прогнозирования и предупреждения геоэкологических и техногенных катастроф Кубанского государственного университета

e-mail: gem@kubsu.ru

Vladimir S. Evdokimov

магистрант Кубанского государственного университета

e-mail: evdok_vova@mail.ru

Aleksand G. Zaretsky

студент Кубанского государственного университета

e-mail: sam_one@mail.ru

Olga A. Bushueva

аспирантка факультета компьютерных технологий и математики Кубанского государственного университета

e-mail: olyabushuyeva@gmail.com

References

  1. Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M., On the possibility of predicting some types of earthquake by a mechanical approach. Acta Mechanica, 2018, vol. 229, iss. 5, pp. 2163–2175. DOI 10.1007/s00707-017-2092-0
  2. Babeshko, V.A., Evdokimova, O.V., Babeshko O.M., On a mechanical approach to the prediction of earthquakes during horizontal motion of lithospheric plates. Acta Mechanica, 2018, vol. 229, iss. 11. pp. 4727–4739. DOI 10.1007/s00707-018-2255-7
  3. Бабешко, В.А., Бабешко, О.М., Евдокимова, О.В., Об одном новом типе трещин, дополняющих трещины Гриффитса–Ирвина. Доклады Академии наук, 2019, vol. 485, №2, с. 34–38. [Babeshko, V.A., Babeshko, O.M., Evdokimova, O.V., A new type of cracks adding to Griffith-Irwin cracks. Dokl. Phys., 2019, vol. 64, pp. 102–105. DOI 10.1134/S1028335819030042]
  4. Griffith, A., VI. The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London. Series A, vol. 221, pp. 163–198. DOI 10.1098/rsta.1921.0006
  5. Sator C., Becker W., Closed-form solutions for stress singularities at plane bi- and trimaterial junctions. Arch. Appl. Mech., 2012, vol. 82, pp. 643–658. DOI 10.1007/s00419-011-0580-6
  6. Irwin, G., Fracture dynamics. In: Fracture of metals. ASM, Cleveland, 1948, p. 147–166.
  7. Leblond, J.B., Frelat J., Crack kinking from an interface crack with initial contact between the cracks lips. Europ. J. Mech. A. Solids, 2001, vol. 20, pp. 937–951.
  8. Loboda, V.V., Sheveleva, A.E., Determining prefracture zones at a crack tip between two elastic orthotropic bodies. Int. Appl. Mech., 2003, vol. 39, iss. 5, p. 566–572. DOI 10.1023/A:1025139625891
  9. Loeber, J.F., Sih, G.C., Transmission of anti-plane shear waves past an interface crack in dissimilar media. Engineering Fracture Mechanics, 1973, vol. 146, pp. 699–725. DOI 10.1016/0013-7944(73)90048-9
  10. Menshykov, O.V., Menshykov, M.V., Guz, I.A., An iterative BEM for the dynamic analysis of interface crack contact problems. Engineering Analysis with Boundary Elements, 2011, vol. 35, iss. 5, pp. 735–749. DOI 10.1016/j.enganabound.2010.12.005
  11. Mikhas'kiv, V.V., Butrak, I.O., Stress concentration around a spheroidal crack coused by a harmonic wave incident at an arbitrary angle. Int. Appl. Mech., 2006, vol. 42, iss. 1, pp. 61–66. DOI 10.1007/s10778-006-0059-2
  12. Rice, J.R., Elastic fracture mechanics concepts for interface cracks. Trans. ASME. J. Appl. Mech., 1988, vol. 55, pp. 98–103. DOI 10.1115/1.3173668
  13. Zhang, Ch., Gross, D., On wave propagation in elastic solids with cracks. Comp. Mech. Publ., Southampton, UK, Boston, USA, 1998.
  14. Морозов, Н.Ф., Математические вопросы теории трещин. Наука, Москва, 1984. [Morozov, N.F., Matematicheskie voprosy teorii treshchin = Mathematical issues in crack theory. Nauka, Moscow, 1984. (in Russian)]
  15. Черепанов, Г.П., Механика хрупкого разрушения. Наука, Москва, 1974. [Cherepanov, G.P., Mekhanika khrupkogo razrusheniya = A mechanics of brittle fracture. Nauka, Moscow, 1974. (in Russian)]
  16. Kirugulige, M.S., Tippur H.V., Mixed-mode dynamic crack growth in functionally graded glass-filled epoxy. Exp Mech., 2006, vol. 46, iss. 2, pp. 269–281. DOI 10.1007/s11340-006-5863-4
  17. Huang, Y., Gao, H., Intersonic crack propagation – Part II: Suddenly stopping crack. J. Appl. Mech., 2002, vol. 69, pp. 76–80. DOI 10.1115/1.1410936
  18. Бабешко, В.А., Евдокимова, О.В., Бабешко, О.М., Об интегральных уравнениях трещин нового типа. Вестник Санкт-Петербургского университета математика, механика, астрономия, 2022, vol. 55, no. 3, pp. 267–274. [Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M., On integral equations for cracks of a new type. Vestnik Sankt-Peterburgskogo universiteta matematika, mekhanika, astronomiya = Bulletin of Saint Petersburg University Mathematics, Mechanics, Astronomy, 2022, vol. 55, no. 3, pp. 267–274. (in Russian)] DOI 10.21638/spbu01.2022.302
  19. Бабешко, В.А., Евдокимова, О.В., Бабешко, О.М., Фрактальные свойства блочных элементов и новый универсальный метод моделирования. Доклады Академии наук, 2021, т. 499, с. 21–26. [Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M., Fractal properties of block elements and a new universal modeling method. Doklady Akademii nauk = Rep. of the Academy of Sciences, 2021, vol. 499, pp. 21–26. (in Russian)] DOI 10.31857/S2686740021040039
  20. Ворович, И.И., Бабешко, В.А., Динамические смешанные задачи теории упругости для неклассических областей. Наука, Москва, 1979. [Vorovich, I.I., Babeshko, V.A., Dinamicheskie smeshannye zadachi teorii uprugosti dlya neklassicheskikh oblastey = Dynamic mixed problems of elasticity theory for nonclassical domains. Nauka, Moscow, 1979. (in Russian)]
  21. Бабешко, В.А., Евдокимова, О.В., Бабешко, О.М., Метод блочного элемента в разложении решений сложных граничных задач механики. Доклады Академии наук, 2020, т. 495, с. 34–38. [Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M., The block element method in the expansion of solutions to complex boundary value problems in mechanics. Doklady Akademii nauk = Rep. of the Academy of Sciences, 2020, vol. 495, p. 34–38. (in Russian)] DOI 10.31857/S2686740020060048

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Issue

2022. Vol. 19. No. 4

Section

Mechanics

Pages

37-47

Submitted

2022-11-15

Published

2022-11-30

How to Cite

Babeshko O.M., Evdokimova O.V., Babeshko V.A., Gorshkova E.M., Evdokimov V.S., Zaretsky A.G., Bushueva O.A. Development of a method for assessing the stability of a new type of crack, the conditions of destruction of the medium and decomposability by simple solutions. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2022, vol. 19, no. 4, pp. 37-47. DOI: https://doi.org/10.31429/vestnik-19-4-37-47 (In Russian)

Copyright (c) 2022 Babeshko O.M., Evdokimova O.V., Babeshko V.A., Gorshkova E.M., Evdokimov V.S., Zaretsky A.G., Bushueva O.A.

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