- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 396745, 22 pages
A Quasistatic Contact Problem for Viscoelastic Materials with Slip-Dependent Friction and Time Delay
1Department of Mathematics, Sichuan University, Chengdu 610064, China
2Department of Mathematics, Kunming University, Kunming 650221, China
Received 27 June 2012; Revised 26 September 2012; Accepted 16 November 2012
Academic Editor: Marco Paggi
Copyright © 2012 Si-sheng Yao and Nan-jing Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- W. Han and M. Sofonea, Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity, vol. 30 of Studies in Advanced Mathematics, American Mathematical Society/ International Press, Providence, RI, USA, 2002.
- X. W. Chen, X. L. Han, and F. Luo S Wu, “Fiber element based elastic-plastic analysis procedure and engineering application,” Procedia Engineering, vol. 14, pp. 1807–1815, 2011.
- O. Markus and P. Terhi, “Computational framework for common visco-elastic models in engineering based on the theory of rheology,” Computers and Geotechnics, vol. 42, pp. 145–156, 2012.
- P. R. Marur, “An engineering approach for evaluating effective elastic moduli of particulate composites,” Materials Letters, vol. 58, no. 30, pp. 3971–3975, 2004.
- I. Argatov, “Sinusoidally-driven flat-ended indentation of time-dependent materials: asymptotic models for low and high rate loading,” Mechanics of Materials, vol. 48, pp. 56–70, 2012.
- F. Maceri, M. Marino, and G. Vairo, “An insight on multiscale tendon modeling in muscle-tendon integrated behavior,” Biomechanics and Modeling in Mechanobiology, vol. 11, no. 3-4, pp. 505–517, 2012.
- D. Duvaut and J. L. Lions, Inequalities in Mechanics and Physics, Springer, Berlin, Germany, 1976.
- N. Kikuchi and J. T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, vol. 8, SIAM, Philadelphia, Pa, USA, 1988.
- O. Chau, J. R. Fernández, M. Shillor, and M. Sofonea, “Variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion,” Journal of Computational and Applied Mathematics, vol. 159, no. 2, pp. 431–465, 2003.
- A. Rodriguez-Aros, M. Sofonea, and J. Viano, “A class of evolutionary variational inequalities with volterratype integral term,” Mathematical Models and Methods in Applied Sciences, vol. 14, pp. 555–577, 2004.
- M. Shillor, “Special issue on recent advances in contact mechanics,” Mathematical and Computer Modelling, vol. 28, pp. 4–8, 1998.
- W. Han and M. Sofonea, “Evolutionary variational inequalities arising in viscoelastic contact problems,” SIAM Journal on Numerical Analysis, vol. 38, no. 2, pp. 556–579, 2000.
- O. Chau, D. Motreanu, and M. Sofonea, “Quasistatic frictional problems for elastic and viscoelastic materials,” Applications of Mathematics, vol. 47, no. 4, pp. 341–360, 2002.
- M. Delost and C. Fabre, “On abstract variational inequalities in viscoplasticity with frictional contact,” Journal of Optimization Theory and Applications, vol. 133, no. 2, pp. 131–150, 2007.
- E. A. H. Vollebregt and H. M. Schuttelaars, “Quasi-static analysis of two-dimensional rolling contact with slip-velocity dependent friction,” Journal of Sound and Vibration, vol. 331, pp. 2141–2155, 2012.
- M. Shillor, M. Sofonea, and J. J. Telega, Models and Analysis of Quasistatic Contact, vol. 655 of Lecture Notes in Physics, Springer, Berlin, Germany, 2004.
- S. Migórski, A. Ochal, and M. Sofonea, “An evolution problem in nonsmooth elasto-viscoplasicity,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 12, pp. e2766–e2771, 2009.
- S. Migórski, A. Ochal, and M. Sofonea, “History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3384–3396, 2011.
- N. Costea and A. Matei, “Contact models leading to variational-hemivariational inequalities,” Journal of Mathematical Analysis and Applications, vol. 386, no. 2, pp. 647–660, 2012.
- V. Comincioli, “A result concerning a variational inequality of evolution for operators of first order in t with retarded terms,” Annali di Matematica Pura ed Applicata, vol. 88, pp. 357–378, 1971.
- J. Y. Park, J. U. Jeong, and Y. H. Kang, “Optimal control of parabolic variational inequalities with delays and state constraint,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 12, pp. e329–e339, 2009.
- S. W. Zhu, “Optimal control of variational inequalities with delays in the highest order spatial derivatives,” Acta Mathematica Sinica, vol. 22, no. 2, pp. 607–624, 2006.
- J. M. Yong and L. P. Pan, “Quasi-linear parabolic partial differential equations with delays in the highest order spatial derivatives,” Australian Mathematical Society, vol. 54, no. 2, pp. 174–203, 1993.
- M. Sofonea, A. Rodríguez-Arós, and J. M. Viaño, “A class of integro-differential variational inequalities with applications to viscoelastic contact,” Mathematical and Computer Modelling, vol. 41, no. 11-12, pp. 1355–1369, 2005.
- M. Campo, J. R. Fernández, and Á. Rodríguez-Arós, “A quasistatic contact problem with normal compliance and damage involving viscoelastic materials with long memory,” Applied Numerical Mathematics, vol. 58, no. 9, pp. 1274–1290, 2008.
- I. Figueiredo and L. Trabucho, “A class of contact and friction dynamic problems in thermoelasticity and in thermoviscoelasticity,” International Journal of Engineering Science, vol. 33, no. 1, pp. 45–66, 1995.
- A. Kulig and S. Migórski, “Solvability and continuous dependence results for second order nonlinear evolution inclusions with a Volterra-type operator,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 13, pp. 4729–4746, 2012.
- A. Rodrıguez-Aros, M. Sofonea, and J. Viano, “Numerical analysis of a frictional contact problem for viscoelastic materials with long-term memory,” Advances in Mechanics and Mathematics, vol. 18, pp. 1–11, 2009.