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Analysis of two quasistatic history-dependent contact models
1. | Department of Mathematics, Zhejiang University, Hangzhou 310027, China |
2. | Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Łojasiewicza 6, 30348 Krakow |
3. | Laboratoire de Mathématiques et Physique pour les Systèmes, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan |
References:
[1] |
H. T. Banks, S. Hu and Z. R. Kenz, A brief review of elasticity and viscoelasticity for solids,, Adv. Appl. Math. Mech., 3 (2011), 1.
|
[2] |
H. T. Banks, G. A. Pinter, L. K. Potter, J. M. Gaitens and L. C. Yanyo, Modeling of quasistatic and dynamic load responses of filled viesoelastic materials,, Chapter 11 in Mathematical Modeling: Case Studies from Industry (eds. E. Cumberbatch and A. Fitt), (2011), 229. Google Scholar |
[3] |
H. T. Banks, G. A. Pinter, L. K. Potter, B. C. Munoz and L. C. Yanyo, Estimation and control related issues in smart material structure and fluids,, Optimization Techniques and Applications, (1998), 19. Google Scholar |
[4] |
F. H. Clarke, Optimization and Nonsmooth Analysis,, Wiley, (1983).
|
[5] |
N. Cristescu and I. Suliciu, Viscoplasticity,, Martinus Nijhoff Publishers, (1982).
|
[6] |
Z. Denkowski, S. Migórski and N. S. Papageorgiou, An Introduction to Nonlinear Analysis: Theory,, Kluwer Academic/Plenum Publishers, (2003).
|
[7] |
Z. Denkowski, S. Migórski and N. S. Papageorgiou, An Introduction to Nonlinear Analysis: Applications,, Kluwer Academic/Plenum Publishers, (2003).
|
[8] |
A. D. Drozdov, Finite Elasticity and Viscoelasticity-A Course in the Nonlinear Mechanics of Solids,, World Scientific, (1996).
doi: 10.1142/2905. |
[9] |
C. Eck, J. Jarušek and M. Krbeč, Unilateral Contact Problems: Variational Methods and Existence Theorems,, Pure and Applied Mathematics, (2005).
doi: 10.1201/9781420027365. |
[10] |
A. Farcaş, F. Pătrulescu and M. Sofonea, A history-dependent contact problem with unilateral constraint,, Mathematics and its Applications, 2 (2012), 105. Google Scholar |
[11] |
W. Han and M. Sofonea, Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity,, Studies in Advanced Mathematics, (2002).
|
[12] |
I. R. Ionescu and M. Sofonea, Functional and Numerical Methods in Viscoplasticity,, Oxford University Press, (1993).
|
[13] |
A. Klarbring, A. Mikelic and M. Shillor, Frictional contact problems with normal compliance,, Int. J. Engng. Sci., 26 (1988), 811.
doi: 10.1016/0020-7225(88)90032-8. |
[14] |
A. Kulig and S. Migórski, Solvability and continuous dependence results for second order nonlinear evolution inclusions with a Volterra-type operator,, Nonlinear Analysis, 75 (2012), 4729.
doi: 10.1016/j.na.2012.03.023. |
[15] |
J. A. C. Martins and J. T. Oden, Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws,, Nonlinear Analysis TMA, 11 (1987), 407.
doi: 10.1016/0362-546X(87)90055-1. |
[16] |
S. Migórski, Dynamic hemivariational inequality modeling viscoelastic contact problem with normal damped response and friction,, Applicable Analysis, 84 (2005), 669.
doi: 10.1080/00036810500048129. |
[17] |
S. Migórski and A. Ochal, A unified approach to dynamic contact problems in viscoelasticity,, Journal of Elasticity, 83 (2006), 247.
doi: 10.1007/s10659-005-9034-0. |
[18] |
S. Migórski, A. Ochal and M. Sofonea, History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics,, Nonlinear Anal. Real World Appl., 12 (2011), 3384.
doi: 10.1016/j.nonrwa.2011.06.002. |
[19] |
S. Migórski, A. Ochal and M. Sofonea, Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems,, Advances in Mechanics and Mathematics, (2013).
doi: 10.1007/978-1-4614-4232-5. |
[20] |
J. T. Oden and J. A. C. Martins, Models and computational methods for dynamic friction phenomena,, Computer Methods in Applied Mechanics and Engineering, 52 (1985), 527.
doi: 10.1016/0045-7825(85)90009-X. |
[21] |
P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications,, Birkhäuser, (1985).
doi: 10.1007/978-1-4612-5152-1. |
[22] |
P. D. Panagiotopoulos, Hemivariational Inequalities, Applications in Mechanics and Engineering,, Springer-Verlag, (1993).
doi: 10.1007/978-3-642-51677-1. |
[23] |
J. Piotrowski, Smoothing dry friction damping by dither generated in rolling contact of wheel and rail and its influence on ride dynamics of freight wagons,, Vehicle System Dynamics, 48 (2010), 675.
doi: 10.1080/00423110903126478. |
[24] |
M. Shillor, M. Sofonea and J. J. Telega, Models and Analysis of Quasistatic Contact,, Springer, (2004).
doi: 10.1007/b99799. |
[25] |
M. Sofonea and A. Matei, Mathematical Models in Contact Mechanics,, London Mathematical Society Lecture Note Series, (2012).
doi: 10.1017/CBO9781139104166. |
[26] |
M. Sofonea and F. Pätrulescu, Analysis of a history-dependent frictionless contact problem,, Mathematics and Mechanics of Solids, 18 (2013), 409.
doi: 10.1177/1081286512440004. |
[27] |
M. Sofonea and M. Shillor, A viscoplastic contact problem with a normal compliance with limited penetration condition and history-dependent stiffness coefficient,, Communications in Pure and Appled Analysis, 13 (2014), 371.
doi: 10.3934/cpaa.2014.13.371. |
show all references
References:
[1] |
H. T. Banks, S. Hu and Z. R. Kenz, A brief review of elasticity and viscoelasticity for solids,, Adv. Appl. Math. Mech., 3 (2011), 1.
|
[2] |
H. T. Banks, G. A. Pinter, L. K. Potter, J. M. Gaitens and L. C. Yanyo, Modeling of quasistatic and dynamic load responses of filled viesoelastic materials,, Chapter 11 in Mathematical Modeling: Case Studies from Industry (eds. E. Cumberbatch and A. Fitt), (2011), 229. Google Scholar |
[3] |
H. T. Banks, G. A. Pinter, L. K. Potter, B. C. Munoz and L. C. Yanyo, Estimation and control related issues in smart material structure and fluids,, Optimization Techniques and Applications, (1998), 19. Google Scholar |
[4] |
F. H. Clarke, Optimization and Nonsmooth Analysis,, Wiley, (1983).
|
[5] |
N. Cristescu and I. Suliciu, Viscoplasticity,, Martinus Nijhoff Publishers, (1982).
|
[6] |
Z. Denkowski, S. Migórski and N. S. Papageorgiou, An Introduction to Nonlinear Analysis: Theory,, Kluwer Academic/Plenum Publishers, (2003).
|
[7] |
Z. Denkowski, S. Migórski and N. S. Papageorgiou, An Introduction to Nonlinear Analysis: Applications,, Kluwer Academic/Plenum Publishers, (2003).
|
[8] |
A. D. Drozdov, Finite Elasticity and Viscoelasticity-A Course in the Nonlinear Mechanics of Solids,, World Scientific, (1996).
doi: 10.1142/2905. |
[9] |
C. Eck, J. Jarušek and M. Krbeč, Unilateral Contact Problems: Variational Methods and Existence Theorems,, Pure and Applied Mathematics, (2005).
doi: 10.1201/9781420027365. |
[10] |
A. Farcaş, F. Pătrulescu and M. Sofonea, A history-dependent contact problem with unilateral constraint,, Mathematics and its Applications, 2 (2012), 105. Google Scholar |
[11] |
W. Han and M. Sofonea, Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity,, Studies in Advanced Mathematics, (2002).
|
[12] |
I. R. Ionescu and M. Sofonea, Functional and Numerical Methods in Viscoplasticity,, Oxford University Press, (1993).
|
[13] |
A. Klarbring, A. Mikelic and M. Shillor, Frictional contact problems with normal compliance,, Int. J. Engng. Sci., 26 (1988), 811.
doi: 10.1016/0020-7225(88)90032-8. |
[14] |
A. Kulig and S. Migórski, Solvability and continuous dependence results for second order nonlinear evolution inclusions with a Volterra-type operator,, Nonlinear Analysis, 75 (2012), 4729.
doi: 10.1016/j.na.2012.03.023. |
[15] |
J. A. C. Martins and J. T. Oden, Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws,, Nonlinear Analysis TMA, 11 (1987), 407.
doi: 10.1016/0362-546X(87)90055-1. |
[16] |
S. Migórski, Dynamic hemivariational inequality modeling viscoelastic contact problem with normal damped response and friction,, Applicable Analysis, 84 (2005), 669.
doi: 10.1080/00036810500048129. |
[17] |
S. Migórski and A. Ochal, A unified approach to dynamic contact problems in viscoelasticity,, Journal of Elasticity, 83 (2006), 247.
doi: 10.1007/s10659-005-9034-0. |
[18] |
S. Migórski, A. Ochal and M. Sofonea, History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics,, Nonlinear Anal. Real World Appl., 12 (2011), 3384.
doi: 10.1016/j.nonrwa.2011.06.002. |
[19] |
S. Migórski, A. Ochal and M. Sofonea, Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems,, Advances in Mechanics and Mathematics, (2013).
doi: 10.1007/978-1-4614-4232-5. |
[20] |
J. T. Oden and J. A. C. Martins, Models and computational methods for dynamic friction phenomena,, Computer Methods in Applied Mechanics and Engineering, 52 (1985), 527.
doi: 10.1016/0045-7825(85)90009-X. |
[21] |
P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications,, Birkhäuser, (1985).
doi: 10.1007/978-1-4612-5152-1. |
[22] |
P. D. Panagiotopoulos, Hemivariational Inequalities, Applications in Mechanics and Engineering,, Springer-Verlag, (1993).
doi: 10.1007/978-3-642-51677-1. |
[23] |
J. Piotrowski, Smoothing dry friction damping by dither generated in rolling contact of wheel and rail and its influence on ride dynamics of freight wagons,, Vehicle System Dynamics, 48 (2010), 675.
doi: 10.1080/00423110903126478. |
[24] |
M. Shillor, M. Sofonea and J. J. Telega, Models and Analysis of Quasistatic Contact,, Springer, (2004).
doi: 10.1007/b99799. |
[25] |
M. Sofonea and A. Matei, Mathematical Models in Contact Mechanics,, London Mathematical Society Lecture Note Series, (2012).
doi: 10.1017/CBO9781139104166. |
[26] |
M. Sofonea and F. Pätrulescu, Analysis of a history-dependent frictionless contact problem,, Mathematics and Mechanics of Solids, 18 (2013), 409.
doi: 10.1177/1081286512440004. |
[27] |
M. Sofonea and M. Shillor, A viscoplastic contact problem with a normal compliance with limited penetration condition and history-dependent stiffness coefficient,, Communications in Pure and Appled Analysis, 13 (2014), 371.
doi: 10.3934/cpaa.2014.13.371. |
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