On a new type of cracks in vector boundary problems

Authors

  • Babeshko O.M. Kuban State University, Krasnodar, Российская Федерация ORCID 0000-0003-1869-5413
  • Gorshkova E.M. Kuban State University, Krasnodar, Российская Федерация ORCID 0000-0002-2415-6224
  • Zaretskiy A.G. Kuban State University, Krasnodar, Российская Федерация
  • Evdokimov V.S. Kuban State University, Krasnodar, Российская Федерация
  • Khripkov D.A. Kuban State University, Krasnodar, Российская Федерация ORCID 0000-0002-2161-121X

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-20-3-30-36

Abstract

The paper considers the possibility of studying the behavior of a new type of crack in a multilayer medium of complex rheology described by a vector boundary value problem. It is assumed that the cracks of the new type are located perpendicular to the boundary of the multilayer medium. The block element method is applied. Earlier, the authors studied the case when the crack banks are modeled by absolutely rigid semi-infinite plates. Such a contact problem is solved precisely. Based on it, a method of modeling cracks with deformable stamps of simple rheology is being developed. For the case of modeling a crack in a medium described by a vector boundary value problem, an algorithm is proposed that allows the transition to media of higher rheologies. This is achieved by the fractal new universal modeling method developed by the authors.

Keywords:

new type cracks, contact problem, integral equation, complex rheology, vector boundary value problems

Acknowledgement

The work was financially supported by the Russian Science Foundation (project no. 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

Elena M. Gorshkova

канд. физ.-мат. наук, старший научный сотрудник Научно-исследовательской части Кубанского государственного университета

e-mail: gem@kubsu.ru

Aleksandr G. Zaretskiy

студент Кубанского государственного университета

e-mail: sam_one@mail.ru

Vladimir S. Evdokimov

студент Кубанского государственного университета, лаборант Южного научного центра РАН

e-mail: evdok_vova@mail.ru

Dmitry A. Khripkov

научный сотрудник Кубанского государственного университета

e-mail: vestnik@fpm.kubsu.ru

References

  1. Griffith, A., The phenomena of rupture in solids. Trans. Roy. Soc., 1920, vol. 221A, pp. 163–197.
  2. 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.
  3. Irwin, G., Fracture dynamics. Fracture of metals, American Society of Metals, Cleveland, 1948, pp. 147–166.
  4. 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.
  5. Loboda, V.V., Sheveleva, A.E., Determing prefracture zones at a crack tip between two elastic orthotropic bodies. Int. Appl. Mech, 2003, vol. 39, iss. 5, pp. 566–572.
  6. 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.
  7. Menshykov, O.V., Menshykov, M.V., Guz, I.A., Elastodynamics contact problem for an interface crack under harmonic loading. Engineering Fracture Mechanics, 2012, vol. 80, pp. 52–59.
  8. Menshykov, O.V., Menshykov, M.V., Guz, I.A., Mickucka, V., 2-D and 3-D contact problems for interface cracks under harmonic loading. In: Constanda, C. Harris, P.J. (eds.), Integral Methods in Science and Engineering: Computational and Analystic Aspects. New York, Dordrecht, Springer, 2011, pp. 241–252.
  9. Menshykov, O.V., Menshykov, M.V., Guz, I.A., Linear interface crack under plane share wave. CMES (Computer model in Eng. and Sci.), 2009, vol. 48, iss. 2, pp. 107–120.
  10. Menshykov, O.V., Menshykov, M.V., Guz, I.A., Modelling crack closure for an interface crack under harmonic loading. Int. J. of fracture, 2010, vol. 165, pp. 127–134.
  11. 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.
  12. 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.
  13. Rice, J.R., Elastic fracture mechanics concepts for interface cracks. Trans. ASME. J. Appl. Mech., 1988, vol. 55, pp. 98–103.
  14. Zhang, Ch., Gross, D., On wave propagation in elastic solids with cracks. Southampton, Boston, Computational Mechanics Publications, 1998.
  15. Морозов, Н.Ф., Математические вопросы теории трещин. Москва, Наука, 1984. [Morozov, N.F., Matematicheskie voprosy teorii treshchin = Mathematical problems in the theory of cracks. Moscow, Nauka, 1984. (in Russian)]
  16. Черепанов, Г.П., Механика хрупкого разрушения. Москва, Наука, 1974. [Cherepanov, G.P., Mekhanika khrupkogo razrusheniya = Brittle Fracture Mechanics. Moscow, Nauka, 1974. (in Russian)]
  17. 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.
  18. Huang Y., Gao H. Intersonic crack propagation – Part II: Suddenly stopping crack. J. Appl. Mech., 2002, vol. 69, pp. 76–80.
  19. Antipov, Y.A., Smirnov, A.V., Subsonic propagation of a crack parallel to the boundary of a half-plane. Math. Mech. Solids, 2013, vol. 18, pp. 153–167.
  20. Sinclair, G.B., Stress singularities in classical elasticity I. Appl. Mechanics Reviews, 2004, vol. 57, pp. 251–298.
  21. Sinclair, G.B., Stress singularities in classical elasticity II. Appl. Mechanics Reviews, 2004, vol. 57, pp. 385–439.
  22. Бабешко, В.А., Евдокимова, О.В., Бабешко, О.М., Фрактальные свойства блочных элементов и новый универсальный метод моделирования. ДАН, 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.] DOI: 10.31857/S2686740021040039
  23. Ворович, И.И., Бабешко, В.А., Динамические смешанные задачи теории упругости для неклассических областей. Москва, Наука, 1979. [Vorovich, I.I., Babeshko, V.A., Dinamicheskie smeshannye zadachi teorii uprugosti dlya neklassicheskikh oblastey = Dynamic mixed problems of elasticity theory for nonclassical domains. Moscow, Nauka, 1979. (in Russian)]
  24. Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M., Earthquakes and cracks of new type complementing the Griffith-Irvin's crack. Chapter 2. In: Altenbach, H., Eremeyev, V.A., Igumnov, L.A. (eds.), Advanced Structured Materials. Springer, 2021, pp. 11–26. DOI: 10.1007/978-3-030-54928-2
  25. Бабешко, В.А., Евдокимова, О.В., Бабешко, О.М., Зарецкая, М.В., Евдокимов, В.С., О контактных задачах с деформируемым штампом и изменяемой реологией. Вестник Санкт-Петербургского университета. Математика, механика, астрономия, 2023, vol. 55, № 3, с. 267–274. [Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M., Zaretskaya, M.V., Evdokimov, V.S., On contact problems with a deformable punch and variable rheology. Vestnik Sankt-Peterburgskogo universiteta. Matematika, mekhanika, astronomiya = Bulletin of St. Petersburg University. Mathematics, Mechanics, Astronomy, 2023, vol. 55, no. 3, pp. 267–274. (in Russian)] DOI: 10.21638/spbu01.2023.302

Downloads

Issue

2023. Vol. 20. No. 3

Section

Mechanics

Pages

30-36

Submitted

2023-08-16

Published

2023-09-29

How to Cite

Babeshko O.M., Gorshkova E.M., Zaretskiy A.G., Evdokimov V.S., Khripkov D.A. On a new type of cracks in vector boundary problems. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2023, vol. 20, no. 3, pp. 30-36. DOI: https://doi.org/10.31429/vestnik-20-3-30-36 (In Russian)

Copyright (c) 2023 Babeshko O.M., Gorshkova E.M., Zaretskiy A.G., Evdokimov V.S., Khripkov D.A.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.