Abstract:
The equilibrium problem for an elastic body containing a crack on the interface between two media is considered. It is proved that there exist invariant (independent of the integration surface) integrals in this problem. The existence of invariant integrals is also established in the problem of a contact between an elastic body and a rigid stamp. Nonlinear boundary conditions of mutual non-penetration are prescribed on the contact boundaries. The physical meaning of invariant integrals is established.
Citation:
A. M. Khludnev, “Invariant integrals in the problem of a crack on the interface between two media”, Prikl. Mekh. Tekh. Fiz., 46:5 (2005), 123–137; J. Appl. Mech. Tech. Phys., 46:5 (2005), 717–729
\Bibitem{Khl05}
\by A.~M.~Khludnev
\paper Invariant integrals in the problem of a crack on the interface between two media
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2005
\vol 46
\issue 5
\pages 123--137
\mathnet{http://mi.mathnet.ru/pmtf2309}
\elib{https://elibrary.ru/item.asp?id=15175973}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2005
\vol 46
\issue 5
\pages 717--729
\crossref{https://doi.org/10.1007/s10808-005-0129-y}
Linking options:
https://www.mathnet.ru/eng/pmtf2309
https://www.mathnet.ru/eng/pmtf/v46/i5/p123
This publication is cited in the following 6 articles:
Alexey Furtsev, Hiromichi Itou, Evgeny Rudoy, “Modeling of bonded elastic structures by a variational method: Theoretical analysis and numerical simulation”, International Journal of Solids and Structures, 182-183 (2020), 100
M. Viswanath, R. Seetharaman, D. Nedumaran, 2019 11th International Conference on Advanced Computing (ICoAC), 2019, 259
V.V. Shcherbakov, “The Griffith formula and J‐integral for elastic bodies with Timoshenko inclusions”, Z Angew Math Mech, 96:11 (2016), 1306
A. N. Guz, I. A. Guz, A. V. Men'shikov, V. A. Men'shikov, “Three-Dimensional Problems in the Dynamic Fracture Mechanics of Materials with Interface Cracks (Review)”, Int Appl Mech, 49:1 (2013), 1
E.M. Rudoy, “Asymptotic behavior of the energy functional for a three-dimensional body with a rigid inclusion and a crack”, J. Appl. Mech. Tech. Phys., 52:2 (2011), 252–263
Alexander Khludnev, Jan Sokołowski, Katarzyna Szulc, “Shape and topological sensitivity analysis in domains with cracks”, Appl Math, 55:6 (2010), 433
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