Overlapping domain problems in the crack theory with possible contact between crack faces
Authors:
Alexander Khludnev and Atusi Tani
Journal:
Quart. Appl. Math. 66 (2008), 423-435
MSC (2000):
Primary 49J40, 49J10, 35J65, 35J70
DOI:
https://doi.org/10.1090/S0033-569X-08-01118-7
Published electronically:
June 6, 2008
MathSciNet review:
2445521
Full-text PDF Free Access
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Abstract: The paper is concerned with the analysis of a new class of overlapping domain problems for elastic bodies having cracks. Inequality type boundary conditions are imposed on the crack faces. We prove an existence of invariant integrals and analyze the asymptotic behavior of the solution. It is shown that the limit problem describes an equilibrium state for the elastic body with a thin inclusion.
References
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- David Kinderlehrer and Guido Stampacchia, An introduction to variational inequalities and their applications, Pure and Applied Mathematics, vol. 88, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. MR 567696
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References
- Parton V. Z., Morozov E. M. Mechanics of elastoplastic fracture. Moscow, Nauka, 1985.
- Morozov N. F. Mathematical questions of a crack theory. Moscow, Nauka, 1984. MR 787610 (87m:73064)
- Cherepanov G. P. Mechanics of brittle fracture. McGraw-Hill, 1973.
- Khludnev A. M., Kovtunenko V. A. Analysis of cracks in solids. Southampton-Boston, WIT Press, 2000.
- Khludnev A. M., Ohtsuka K., Sokolowski J. On derivative of energy functional for elastic bodies with a crack and unilateral conditions. Quarterly Appl. Math., 2002, v. 60, N1, p. 99-109. MR 1878261 (2002i:74021)
- Kovtunenko V. A. Invariant integrals for nonlinear crack problem with possible contact between crack faces. J. Appl. Mat. Mechs, 2003, v. 67, N 1, pp. 109-123. MR 1997626 (2004e:74074)
- Kinderlehrer D., Stampacchia G. An introduction to variational inequalities and their applications. New York, London, Toronto, Sydney, San Francisco, 1980. MR 567696 (81g:49013)
- Grisvard P. Singularities in boundary value problems. Masson, Springer-Verlag. 1991. MR 1173209 (93h:35004)
- Ohtsuka K. Mathematics of brittle fracture. Theoretical studies on fracture mechanics in Japan. Ed. K. Ohtsuka. Hiroshima-Denki Institute of Technology, Hiroshima, 1995. pp. 99-172.
- Maz’ya V., Nazarov S., Plamenevskij B. Asymptotic theory of elliptic boundary value problems in singularly perturbed domains, v. 1, 2. Birkhauser, Basel-Boston-Berlin, 2000.
- Brokate M., Khludnev A. M. On crack propagation shapes in elastic bodies, ZAMP, 2004, v.55, N2, pp. 318-329. MR 2047291 (2005a:74013)
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Additional Information
Alexander Khludnev
Affiliation:
Lavrentyev Institute of Hydrodynamics of the Russian Academy of Sciences, Novosibirsk 630090, Russia
Email:
khlud@hydro.nsc.ru
Atusi Tani
Affiliation:
Department of Mathematics, 3-14-1 Keio University, Yokohama 223-8522, Japan
Email:
tani@math.keio.ac.jp
Received by editor(s):
July 1, 2006
Published electronically:
June 6, 2008
Article copyright:
© Copyright 2008
Brown University
The copyright for this article reverts to public domain 28 years after publication.
