Smooth domain method for crack problems
Authors:
Alexander M. Khludnev and Jan Sokołowski
Journal:
Quart. Appl. Math. 62 (2004), 401-422
MSC:
Primary 35J85; Secondary 35J25, 74B05, 74G99, 74K20
DOI:
https://doi.org/10.1090/qam/2086037
MathSciNet review:
MR2086037
Full-text PDF Free Access
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Abstract: Equilibrium problems for elastic bodies in domains with cracks are considered. Inequality type boundary conditions are imposed at the crack describing a mutual nonpenetration between the crack faces. A new formulation for such problems is proposed in smooth geometrical domains for two-dimensional elasticity and Kirchhoff plates.
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F. Brezzi, M. Fortin, Mixed and hybrid finite element methods, Springer, New York, 1991.
G. P. Cherepanov, Mechanics of brittle fracture, McGraw-Hill, 1979.
M. Dauge, Elliptic boundary value problems on corner domains — smoothness and asymptotics of solutions, Lecture Notes in Mathematics, v.1341, Springer, Berlin, 1988.
R. Duduchava, A. M. Saendig, W. L. Wendland, Interface cracks in anisotropic composites, Math. Methods in Appl. Sciences, 22 (1999), pp. 1413–1446.
P. Grisvard, Elliptic problems in nonsmooth domains, Boston-London-Melbourne, Pitman, 1985.
A. M. Khludnev, V. A. Kovtunenko, Analysis of cracks in solids, Southampton-Boston, WIT Press, 2000.
A. M. Khludnev, J. Sokołowski, Modelling and control in solid mechanics, Basel-Boston-Berlin, Birkhauser, 1997.
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V. Z. Parton, E. M. Morozov, Mechanics of elastoplastic fracture, Moscow, Nauka, 1985 (in Russian).
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R. Temam, Mathematical problems in plasticity, Bordas, Paris, 1985.
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