Crack in a solid under Coulomb friction law

Victor A. Kovtunenko

Applications of Mathematics (2000)

  • Volume: 45, Issue: 4, page 265-290
  • ISSN: 0862-7940

Abstract

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An equilibrium problem for a solid with a crack is considered. We assume that both the Coulomb friction law and a nonpenetration condition hold at the crack faces. The problem is formulated as a quasi-variational inequality. Existence of a solution is proved, and a complete system of boundary conditions fulfilled at the crack surface is obtained in suitable spaces.

How to cite

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Kovtunenko, Victor A.. "Crack in a solid under Coulomb friction law." Applications of Mathematics 45.4 (2000): 265-290. <http://eudml.org/doc/33059>.

@article{Kovtunenko2000,
abstract = {An equilibrium problem for a solid with a crack is considered. We assume that both the Coulomb friction law and a nonpenetration condition hold at the crack faces. The problem is formulated as a quasi-variational inequality. Existence of a solution is proved, and a complete system of boundary conditions fulfilled at the crack surface is obtained in suitable spaces.},
author = {Kovtunenko, Victor A.},
journal = {Applications of Mathematics},
keywords = {variational and quasi-variational inequalities; crack; Coulomb friction; variational and quasi-variational inequalities; crack; Coulomb friction},
language = {eng},
number = {4},
pages = {265-290},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Crack in a solid under Coulomb friction law},
url = {http://eudml.org/doc/33059},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Kovtunenko, Victor A.
TI - Crack in a solid under Coulomb friction law
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 4
SP - 265
EP - 290
AB - An equilibrium problem for a solid with a crack is considered. We assume that both the Coulomb friction law and a nonpenetration condition hold at the crack faces. The problem is formulated as a quasi-variational inequality. Existence of a solution is proved, and a complete system of boundary conditions fulfilled at the crack surface is obtained in suitable spaces.
LA - eng
KW - variational and quasi-variational inequalities; crack; Coulomb friction; variational and quasi-variational inequalities; crack; Coulomb friction
UR - http://eudml.org/doc/33059
ER -

References

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  1. Accounting of a friction in contact elastoplastic problems, In: Fund. Prob. Mat. Mekh. 2, Novosibirsk Univ., 1996. (Russian) (1996) 
  2. Variational and Quasivariational Inequalities. Applications to Free Boundary Problems, Wiley, Chichester, 1984. (1984) MR0745619
  3. On some mechanism of the development of cracks in the Earth solid shell, Izvestiya USSR Acad. Sci., Physics of the Earth 9 (1984), 3–12. (Russian) (1984) 
  4. 10.1007/BF01198487, Integral Equations Operator Theory 23 (1995), 294–335. (1995) MR1356337DOI10.1007/BF01198487
  5. Les Inéquations en Mécanique et en Physique, Dunod, Paris, 1972. (1972) MR0464857
  6. 10.1142/S0218202598000196, Math. Models Methods Appl. Sci. 8 (3) (1998), 445–468. (1998) MR1624879DOI10.1142/S0218202598000196
  7. Singularities in Boundary Value Problems, Masson, Paris & Springer-Verlag, Berlin, 1992. (1992) Zbl0778.93007MR1173209
  8. Solution of Variational Inequalities in Mechanics, Springer-Verlag, New York, 1988. (1988) MR0952855
  9. Contact problems with bounded friction, coercive case, Czechoslovak Math. J. 33 (108) (1983), 237–261. (1983) MR0699024
  10. Modelling and Control in Solid Mechanics, Birkhäuser, Basel-Boston-Berlin, 1997. (1997) MR1433133
  11. Analytical solution of a variational inequality for a cutted bar, Control Cybernet. 25 (1996), 801–808. (1996) Zbl0863.73077MR1420072
  12. Iterative penalty method for plate with a crack, Adv. Math. Sci. Appl. 7 (1997), 667–674. (1997) Zbl0896.73079MR1476271
  13. A variational and a boundary problems with friction on the interior boundary, Siberian Math. J. 39 (1998), 1060–1073. (1998) MR1650748
  14. Variational and Quasivariational Inequalities in Mechanics, MGAPI, Moscow, 1997. (Russian) (1997) 
  15. Problémes aux Limites non Homogénes et Applications 1, Dunod, Paris, 1968. (1968) 
  16. Spaces of S. L. Sobolev, Leningrad Univ., 1985. (Russian) (1985) MR0807364
  17. Mathematical Foundations of the Crack Theory, Nauka, Moscow, 1984. (Russian) (1984) MR0787610
  18. Elliptic Problems in Domains with Piecewise Smooth Boundaries, Nauka, Moscow, 1991. (Russian) (1991) 
  19. On the solution of the variational inequality to the Signorini problem with small friction, Boll. Um. Mat. Ital. 17-B (1980), 796–811. (1980) MR0580559
  20. Mathematical aspects of modelling the macroscopic behaviour of cross-ply laminates with intralaminar cracks, Control Cybernet. 23 (1994), 773–792. (1994) MR1303383
  21. Nonlinear Functional Analysis and its Applications. 1. Fixed-Point Theorems, Springer-Verlag, New York, 1986. (1986) MR0816732

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