About defects in the rigid contact of lithospheric plates to the basement and arbitrary harmonic influences
UDC
539.3EDN
ZXPYLVAbstract
The existence of hidden defects, which are not observed visually, in coatings of nanomaterials, in seismology and in materials science is investigated. A method of investigation of such defects in coatings, based on a topological approach is developed. An analysis of defects is given using the example of an investigation of the stress-strain state of a block structure consisting of two-dimensional horizontally disposed different-type blocks contacting along the boundaries between themselves. The block structure is located on the surface of a three-dimensional linearly deformable substrate and is rigidly connected to it. The considered block structures are under arbitrary harmonic external influence. This is characteristic not only of nanocoatings, surface hardening of materials, but also of lithospheric plates, the investigation of the stress-strain state of which serves the purpose of obtaining information about the seismicity of the territories. The obtained results indicate that the hidden defects are actually new types of cracks, supplementing the known Griffiths-Irwin cracks. Unlike Griffiths-Irwin cracks, characterized by roundness and smoothness of boundaries, this particular type of cracks contains fractures of boundaries and visually more accurately describes crack boundaries, for example, in brittle materials such as, for example, glass.
Keywords:
block element, factorization, topology, integral and differential factorization methods, exterior forms, block structures, boundary problems, bodies with coverings, hidden defectsFunding information
Отдельные фрагменты работы выполнены в рамках реализации Госзадания на 2017 г. проекты (9.8753.2017/БЧ, 0256-2014-0006), Программы президиума РАН 1-33П, проекты с (0256-2015-0088 по 0256-2015-0093), и при поддержке грантов РФФИ (15-01-01379, 15-08-01377, 16-41-230214, 16-41-230218, 16-48-230216, 17-08-00323).
References
- Бабешко О.М. Топологический метод в проблеме оценки концентрации напряжений в разломах литосферных плит // Экологический вестник научных центров Черноморского экономического сотрудниества. 2015. № 2. С. 14-21. [Babeshko O.M. Topologicheskiy metod v probleme otsenki kontsentratsii napryazheniy v razlomakh litosfernykh plit [Topological method in the problem of estimating stress concentration in faults of lithospheric plates]. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudniestva [Ecological bulletin of scientific centers of the Black Sea Economic Cooperation], 2015, no. 2, pp. 14-21. (In Russian)]
- Бабешко В.А., Евдокимова О.В., Бабешко О.М. Топологические методы в теории скрытых дефектов и некоторые аномалии // ДАН. 2014. Т. 457. № 6. С. 650-655. [Babeshko V.A., Evdokimova O.V., Babeshko O.M. Topologicheskie metody v teorii skrytykh defektov i nekotorye anomalii [Topological methods in the theory of hidden defects and some anomalies]. Doklady Akademii nauk [Rep. of the Academy of Sciences], 2014, vol. 457, no 6, pp. 650-655. (In Russian)]
- Бабешко В.А., Евдокимова О.В., Бабешко О.М. Стартовое землетрясение при гармонических воздействиях // ДАН. 2016. Т. 471. № 1. С. 37-40. [Babeshko V.A., Evdokimova O.V., Babeshko O.M. Startovoe zemletryasenie pri garmonicheskikh vozdeystviyakh [Start-up earthquake with harmonic influences]. Doklady Akademii nauk [Rep. of the Academy of Sciences], 2016, vol. 471, no. 1, pp. 37-40. (In Russian)]
- Ворович И.И., Бабешко В.А. Динамические смешанные задачи теории упругости для неклассических областей. М.: Наука, 1979. 320 с. [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 Pub., 1979, 320 p. (In Russian)]
- Cherepanov G.P. Mechanics of Brittle Fracture. New York: McGraw-Hill, 1979. 950 p.
- Черепанов Г.П. Механика разрушения композиционных материалов. М.: Наука, 1983. 296 с. [Cherepanov G.P. Mekhanika razrusheniya kompozitsionnykh materialov [Mechanics of fracture of composite materials]. Moscow, Nauka Pub., 1983, 296 s. (In Russian)]
- Irwin G. Fracture In: Handbuch der Physic, bd 6. Berlin: Springer-Verlag, 1958. 551 p.
- Rice J. Mathematical analysisin the mechanicsof fracture. Treatise on Fracture. Vol. II. Academic Press Int., New York, 1968. P. 191-311.
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Copyright (c) 2017 Бабешко О.М., Бабешко В.А., Евдокимова О.В.
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