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2002 | 12 | 1 | 51-58
Tytuł artykułu

Analysis of a viscoelastic antiplane contact problem with slip-dependent friction

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study a mathematical problem modelling the antiplane shear deformation of a viscoelastic body in frictional contact with a rigid foundation. The contact is bilateral and is modelled with a slip-dependent friction law. We present the classical formulation for the antiplane problem and write the corresponding variational formulation. Then we establish the existence of a unique weak solution to the model, by using the Banach fixed-point theorem and classical results for elliptic variational inequalities. Finally, we prove that the solution converges to the solution of the corresponding elastic problem as the viscosity converges to zero.
Rocznik
Tom
12
Numer
1
Strony
51-58
Opis fizyczny
Daty
wydano
2002
otrzymano
2001-09-01
poprawiono
2002-01-01
Twórcy
  • University of Perpignan, Laboratoire de Théorie des Systèmes, 52 Avenue de Villeneuve, 66860 Perpignan cedex, France
  • University of Craiova, Department of Mathematics, Str. 'Al. I. Cuza' 13, 1100 Craiova, Romania
Bibliografia
  • Andreu F., Mazón J.M. and Sofonea M. (2000): Entropy solutions in the study of antiplane shear deformations for elastic solids. - Math. Models Meth. Appl. Sci. (M^3AS), Vol. 10, No. 1, pp. 96-126.
  • Campillo M. and Ionescu I.R. (1997): Initiation of antiplane shear instability under slip dependent friction. - J.Geophys. Res., Vol. B9, pp. 363-371.
  • Chau O., Han W. and Sofonea M. (2001): Analysis and approximation of a viscoelastic contact problem with slip dependent friction. - Dyn. Cont. Discr. Impuls.Syst., Vol. 8, No. 1, pp. 153-174.
  • Horgan C.O. (1995): Anti-plane shear deformation in linear and nonlinear solid mechanics. - SIAM Rev., Vol. 37, No. 1, pp. 53-81.
  • Horgan C.O. (1995): Decay estimates for boundary-value problems in linear and nonlinear continuum mechanics, In: Mathematical Problems in Elasticity (R. Russo, Ed.). - Singapore: World Scientific, pp. 47-89.
  • Horgan C.O. and Miller K.L. (1994): Anti-plane shear deformation for homogeneous and inhomogeneous anisotropic linearly elastic solids. - J. Appl. Mech., Vol. 61, No. 1, pp. 23-29.
  • Ionescu I.R. and Paumier J.-C. (1996): On the contact problem with slip displacement dependent friction in elastostatics. - Int. J.Eng. Sci., Vol. 34, No. 4, pp. 471-491.
  • Kuttler K.L. and Shillor M. (1999): Set-valued pseudomonotone maps and degenerate evolution equations. - Comm. Contemp. Math., Vol. 1, No. 1, pp. 87-123.
  • Matei A., Motreanu V.V. and Sofonea M. (2001): A Quasistatic Antiplane Contact Problem With Slip Dependent Friction. - Adv. Nonlin. Variat. Ineq., Vol. 4, No. 2, pp. 1-21.
  • Motreanu D. and Sofonea M. (1999): Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials. - Abstr. Appl. Anal., Vol. 4, No. 3, pp. 255-279.
  • Ohnaka M. (1996): Nonuniformity of the constitutive law parameters for shear rupture and quasistatic nucleation to dynamic rupture: A physical model of earthquake generation model. - Earthquake Prediction: The Scientific Challange, Irvine, CA: Acad. of Sci.
  • Rabinowicz E. (1965): Friction and Wear of Materials. -New York: Wiley.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv12i1p51bwm
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