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Modeling a hard, thin curvilinear interface
Dual formulation of a viscoplastic contact problem with unilateral constraint
1. | Departement of Mathematics, University of Craiov, A.I. Cuza Street 13, 200585, Craiova |
2. | Laboratoire de Mathématiques et Physique pour les Systèmes, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan |
References:
[1] |
M. Anders, "Dual-Dual Formulations for Frictional Contact Problems in Mechanics," Ph.D thesis, Leibniz Universität, Hannover, 2011. |
[2] |
B. Awbi, M. Shillor and M. Sofonea, Dual formulation of a quasistatic viscoelastic contact problem with Tresca's friction law, Applicable Analysis, 79 (2001), 1-20.
doi: 10.1080/00036810108840949. |
[3] |
M. Barboteu, A. Matei and M. Sofonea, Analysis of quasistatic viscoplastic contact problems with normal compliance, Q. J. Mechanics Appl. Math., 65 (2012), 555-579.
doi: 10.1093/qjmam/hbs016. |
[4] |
N. Cristescu and I. Suliciu, "Viscoplasticity," Translated from the Romanian, Mechanics of Plastic Solids, 5, Martinus Nijhoff Publishers, The Hague, 1982. |
[5] |
W. Han and M. Sofonea, "Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity," AMS/IP Studies in Advanced Mathematics, 30, Americal Mathematical Society, Providence, RI; International Press, Somerville, MA, 2002. |
[6] |
I. Hlaváček, J. Haslinger, J. Nečas and J. Lovášek, "Solution of Variational Inequalities in Mechanics," Translated from the Slovak by J. Jarník, Applied Mathematical Sciences, 66, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4612-1048-1. |
[7] |
I. R. Ionescu and M. Sofonea, "Functional and Numerical Methods in Viscoplasticity," Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993. |
[8] |
N. Kikuchi and J. T. Oden, "Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods," SIAM Studies in Applied Mathematics, 8, SIAM, Philadelphia, PA, 1988. |
[9] |
M. Shillor, M. Sofonea and J. J. Telega, "Models and Analysis of Quasistatic Contact," Lecture Notes in Physics, 655, Springer, Berlin, 2004.
doi: 10.1007/b99799. |
[10] |
M. Sofonea, C. Avramescu and A. Matei, A fixed point result with applications in the study of viscoplastic frictionless contact problems, Communications on Pure and Applied Analysis, 7 (2008), 645-658.
doi: 10.3934/cpaa.2008.7.645. |
[11] |
M. Sofonea and A. Matei, History-dependent quasi-variational inequalities arising in contact mechanics, European Journal of Applied Mathematics, 22 (2011), 471-491.
doi: 10.1017/S0956792511000192. |
[12] |
J. J. Telega, Topics on unilateral contact problems of elasticity and inelasticity, in "Nonsmooth Mechanics and Applications" (eds. J.-J. Moreau, P. D. Panagiotopoulos and G. Strang), Birkhäuser Verlag, Basel, (1988), 340-461. |
show all references
References:
[1] |
M. Anders, "Dual-Dual Formulations for Frictional Contact Problems in Mechanics," Ph.D thesis, Leibniz Universität, Hannover, 2011. |
[2] |
B. Awbi, M. Shillor and M. Sofonea, Dual formulation of a quasistatic viscoelastic contact problem with Tresca's friction law, Applicable Analysis, 79 (2001), 1-20.
doi: 10.1080/00036810108840949. |
[3] |
M. Barboteu, A. Matei and M. Sofonea, Analysis of quasistatic viscoplastic contact problems with normal compliance, Q. J. Mechanics Appl. Math., 65 (2012), 555-579.
doi: 10.1093/qjmam/hbs016. |
[4] |
N. Cristescu and I. Suliciu, "Viscoplasticity," Translated from the Romanian, Mechanics of Plastic Solids, 5, Martinus Nijhoff Publishers, The Hague, 1982. |
[5] |
W. Han and M. Sofonea, "Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity," AMS/IP Studies in Advanced Mathematics, 30, Americal Mathematical Society, Providence, RI; International Press, Somerville, MA, 2002. |
[6] |
I. Hlaváček, J. Haslinger, J. Nečas and J. Lovášek, "Solution of Variational Inequalities in Mechanics," Translated from the Slovak by J. Jarník, Applied Mathematical Sciences, 66, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4612-1048-1. |
[7] |
I. R. Ionescu and M. Sofonea, "Functional and Numerical Methods in Viscoplasticity," Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993. |
[8] |
N. Kikuchi and J. T. Oden, "Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods," SIAM Studies in Applied Mathematics, 8, SIAM, Philadelphia, PA, 1988. |
[9] |
M. Shillor, M. Sofonea and J. J. Telega, "Models and Analysis of Quasistatic Contact," Lecture Notes in Physics, 655, Springer, Berlin, 2004.
doi: 10.1007/b99799. |
[10] |
M. Sofonea, C. Avramescu and A. Matei, A fixed point result with applications in the study of viscoplastic frictionless contact problems, Communications on Pure and Applied Analysis, 7 (2008), 645-658.
doi: 10.3934/cpaa.2008.7.645. |
[11] |
M. Sofonea and A. Matei, History-dependent quasi-variational inequalities arising in contact mechanics, European Journal of Applied Mathematics, 22 (2011), 471-491.
doi: 10.1017/S0956792511000192. |
[12] |
J. J. Telega, Topics on unilateral contact problems of elasticity and inelasticity, in "Nonsmooth Mechanics and Applications" (eds. J.-J. Moreau, P. D. Panagiotopoulos and G. Strang), Birkhäuser Verlag, Basel, (1988), 340-461. |
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