 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 50, Issue 5 / 2015 | Next article >> |
| A.M. Khludnev, "A Weakly Curved Inclusion in an Elastic Body with Separation," Mech. Solids. 50 (5), 591-601 (2015) |
| Year |
2015 |
Volume |
50 |
Number |
5 |
Pages |
591-601 |
| DOI |
10.3103/S0025654415050106 |
| Title |
A Weakly Curved Inclusion in an Elastic Body with Separation |
| Author(s) |
A.M. Khludnev (Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, pr. Akad. Lavrentyeva 15, Novosibirsk, 630090 Russia, khlud@hydro.nsc.ru) |
| Abstract |
A problem with unknown boundary, which describes the equilibrium of a two-dimensional elastic body with a thin weakly curved inclusion, is studied. The inclusion can separate, thus producing a crack. Nonlinear boundary conditions are posed as inequalities on the crack shores so as to ensure the mutual nonpenetration of the shores. The unique solvability of the problem is proved. The problems of passing to the limit with respect to the thin inclusion rigidity are considered. In particular, a model is constructed by letting the rigidity parameter tend to infinity, and its properties are investigated. On the other hand, it is shown that the zero rigidity parameter of the inclusion exactly corresponds to the problem of equilibrium of an elastic body with a crack satisfying the boundary conditions of mutual nonpenetration of its shores. |
| Keywords |
thin inclusion, crack, nonlinear boundary conditions, inclusion rigidity |
| References |
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| 10. | H. Itou, A. M. Khludnev, E. M. Rudoi, and A. Tani,
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| 12. | A. M. Khludnev and G. Leugering,
"Optimal Control of Cracks in Elastic Bodies with Thin Rigid Inclusions,"
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| 15. | A. M. Khludnev, V. A. Kovtunenko, and A. Tani,
"On the Topological Derivative due to Kink of a Crack with Nonpenetration,"
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94 (6), 571-596 (2010). |
| 16. | A. M. Khludnev,
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No. 5, 98-110 (2010)
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| 24. | A. M. Khludnev and M. Negri,
"Crack on the Boundary of a Thin Elastic Inclusion inside an Elastic Body,"
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92 (5), 341-354 (2012). |
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|
| Received |
13 March 2013 |
| Link to Fulltext |
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