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Frictional contact problems with normal compliance. (English) Zbl 0662.73079
The quasistatic problem of a linear elastic body in unilateral contact with a rigid support subject to Coulomb’s friction law and a power law normal compliance is considered. Two approximations are derived. It is proved that the first, the incremental problem, possesses a solution but it is unique only if it is small and the coefficient of friction is small enough. It is suitable for numerical calculations. The second, the rate problem, captures exactly the path dependence of the quasistatic problem, is more suitable for theoretical investigations and possesses a unique solution for “small” coefficients.

MSC:
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
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[1] Fichera, G., (), 391-424
[2] Nečas, J., Rend. mat., 8, 481, (1975)
[3] Kinderlehrer, D., Ann. scuola N. sup. Pisa IV, 8, 605, (1981)
[4] Kinderlehrer, D., Appl. math. opt., 8, 159, (1982)
[5] Ciarlet, P.G.; Nečas, J., Arch. rat. mech. anal., 87, 319, (1985)
[6] Duvaut, G.; Lions, J.L., Inequalities in mechanics and physics, (1976), Springer Berlin · Zbl 0331.35002
[7] Nečas, J.; Jarušek, J.; Haslinger, J., B.u.m.i., 17-B, 796, (1980), (5)
[8] Jarusek, J., Czech. math. J., 33, 237, (1983)
[9] Jarušek, J., Czech. math. J., 34, 614, (1984)
[10] J. SOKOLOWSKI, Appl. Math. Opt. To appear.
[11] Duvaut, G., C.R. acad. sc. Paris ser. A, 290, 263, (1980)
[12] Oden, J.T.; Pires, E., ()
[13] Oden, J.T.; Pires, E., J. appl. mech., 50, 67, (1983)
[14] Demkowicz, L.; Oden, J.T., Nonlin. anal. th. meth. appl., 6, 10, 1075, (1982)
[15] Cocu, M., Int. J. engng. sci., 22, 5, 567, (1984)
[16] Burdekin, M.; Back, N.; Cowley, A., J. mech. engng. sci., 20, 3, 129, (1978)
[17] Villanueva-Leal, A.; Hinduja, S., (), 9, (4)
[18] Oden, J.T.; Martins, J.A.C., Comput. meth. appl. mech. engng., (1985)
[19] Martins, J.A.C.; Oden, J.T., Nonlin. anal., 11, 3, 407, (1987)
[20] Martins, J.A.C., ()
[21] Klarbring, A., ()
[22] Spence, D.A., (), 249
[23] Spence, D.A., Q. J. mech. appl. math., 39, 323, (1986)
[24] Klarbring, A., ()
[25] Janovský, V., ()
[26] Kikuchi, N.; Oden, J.T., ()
[27] Boieri, P.; Gastaldi, F.; Kinderlehrer, D., Appl. math. opt., 15, 3, 251-277, (1987)
[28] Rabier, P.; Martins, J.A.C.; Oden, J.T.; Campos, L., Int. J. engng sci., 24, 11, 1755, (1986)
[29] Rabier, P.J.; Oden, T.J., Nonlin. anal., 11, (1987), To appear
[30] Johnson, K.L., Contact mechanics, (1985), Cambridge University Press Cambridge · Zbl 0599.73108
[31] Moreau, J.J., (), Cremonse
[32] Ekeland, I.; Temam, R., Convex analysis and variational problems, (1976), North-Holland Amsterdam
[33] Grierson, D.E.; Franchi, A.; De Donato, O.; Corradi, L., Comput. meth. appl. mech. engng, 17/18, 497, (1979)
[34] Adams, R.A., Sobolev spaces, (1975), Academic Press New York · Zbl 0186.19101
[35] A. KLARBRING, A. MIKELIĆ and M. SHILLOR, Nonlin. Anal. Submitted.
[36] Villagio, P., Qualitative methods in elasticity, (1977), Noordhoff
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