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Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 11
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Articles

Fully history-dependent quasivariational inequalities in contact mechanics

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Pages 2464-2484 | Received 19 Jun 2015, Accepted 09 Sep 2015, Published online: 07 Oct 2015

References

  • Baiocchi C, Capelo A. Variational and quasivariational inequalities: applications to free-boundary problems. Chichester: John Wiley; 1984.
  • Brezis H. Equations et inéquations non linéaires dans les espaces vectoriels en dualité [Nonlinear equations and inequalities on vector spaces in duality]. Ann. Inst. Fourier. 1968;18:115–175.
  • Kikuchi N, Oden JT. Theory of variational inequalities with applications to problems of flow through porous media. Int. J. Eng. Sci. 1980;18:1173–1284.
  • Kinderlehrer D, Stampacchia G. An introduction to variational inequalities and their applications. Vol. 31, Classics in applied mathematics. Philadelphia (PA): SIAM; 2000.
  • Panagiotopoulos PD. Inequality problems in mechanics and applications. Boston (MA): Birkhäuser; 1985.
  • Sofonea M, Matei A. Mathematical models in contact mechanics. Vol. 398, London mathematical society lecture note series. Cambridge: Cambridge University Press; 2012.
  • Glowinski R. Numerical methods for nonlinear variational problems. New York (NY): Springer-Verlag; 1984.
  • Hlaváček I, Haslinger J, Necǎs J, et al. Solution of variational inequalities in mechanics. New York (NY): Springer-Verlag; 1988.
  • Kikuchi N, Oden JT. Contact problems in elasticity: a study of variational inequalities and finite element methods. Philadelphia (PA): SIAM; 1988.
  • Duvaut G, Lions JL. Inequalities in mechanics and physics. Berlin: Springer-Verlag; 1976.
  • Eck C, Jarušek J, Krbeč M. Unilateral contact problems: variational methods and existence theorems. Vol. 270, Pure and applied mathematics. New York (NY): Chapman/CRC Press; 2005.
  • Han W, Sofonea M. Quasistatic contact problems in viscoelasticity and viscoplasticity. Vol. 30, Studies in advanced mathematics. Providence (RI), Sommerville (MA): American Mathematical Society, RI-International Press; 2002.
  • Migórski S, Ochal A, Sofonea M. Nonlinear inclusions and hemivariational inequalities. Models and analysis of contact problems. Vol. 26, Advances in mechanics and mathematics. New York (NY): Springer; 2013.
  • Shillor M, Sofonea M, Telega JJ. Models and analysis of quasistatic contact. Variational methods. Vol. 655, Lecture notes in physics. Berlin: Springer; 2004.
  • Han W, Sofonea M. Time-dependent variational inequalities for viscoelastic contact problems. J. Comput. Appl. Math. 2001;136:369–387.
  • Han W, Sofonea M. Evolutionary variational inequalities arising in viscoelastic contact problems. SIAM J. Numer. Anal. 2000;38:556–579.
  • Xiao Y, Huang N, Cho Y. A class of generalized evolution variational inequalities in Banach space. Appl. Math. Lett. 2012;25:914–920.
  • Sofonea M, Matei A. History-dependent quasivariational inequalities arising in contact mechanics. European J. Appl. Math. 2011;22:471–491.
  • Sofonea M, Avramescu C, Matei A. A Fixed point result with applications in the study of viscoplastic frictionless contact problems. Commun. Pure Appl. Anal. 2008;7:645–658.
  • Migórski S, Ochal A, Sofonea M. History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics. Nonlinear Anal. Real World Appl. 2011;12:3384–3396.
  • Banks HT, Hu S, Kenz ZR. A brief review of elasticity and viscoelasticity for solids. Adv. Appl. Math. Mech. 2011;3:1–51.
  • Banks HT, Pinter GA, Potter LK, et al. Estimation and control related issues in smart material structure and fluids. In: Caccetta L, et al., editors. Optimization techniques and applications. Perth: Curtin University Press; 1998. p.19–34.
  • Banks HT, Pinter GA, Potter LK, et al. Modeling of quasistatic and dynamic load responses of filled viscoelastic materials. Chapter 11, In: Cumberbatch E, Fitt A, editors. Mathematical modeling: case studies from industry. Cambridge: Cambridge University Press; 2011. p. 229–252.
  • Oden JT, Martins JAC. Models and computational methods for dynamic friction phenomena. Comput. Methods Appl. Mech. Eng. 1985;52:527–634.
  • Klarbring A, Mikelič A, Shillor M. Frictional contact problems with normal compliance. Int. J. Eng. Sci. 1988;26:811–832.
  • Klarbring A, Mikelič A, Shillor M. On friction problems with normal compliance. Nonlinear Anal. TMA. 1989;13:935–955.
  • Martins JAC, Oden JT. Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws. Nonlinear Anal. TMA. 1987;11:407–428.
  • Amassad A, Shillor M, Sofonea M. A quasistatic contact problem with slip dependent coefficient of friction. Math. Meth. Appl. Sci. 1999;22:267–284.
  • Rochdi M, Shillor M, Sofonea M. A quasistatic viscoelastic contact problem with normal compliance and friction. J. Elast. 1998;51:105–126.
  • Sofonea M, Farcas A. Analysis of a history-dependent frictional contact problem. Appl. Anal. 2014;93:428–444.
  • Sofonea M, Shillor M. A viscoplastic contact problem with a normal compliance with limited penetration conditon and history-dependent stiffness coefficient. Commun. Pure Appl. Anal. 2014;13:371–387.
  • Jarušek J, Sofonea M. On the solvability of dynamic elastic-visco-plastic contact problems. ZAMM-Z. Angew. Math. Me. 2008;88:3–22.

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