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Contact problem with instantaneous normal response friction in viscoelasticity with long-term memory body | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 28 اردیبهشت 1405 اصل مقاله (465.25 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.32371.4812 | ||
| نویسندگان | ||
| Ahmed Hamidat* 1؛ Adel Aissaoui2 | ||
| 1Laboratory of Operator Theory and PDE: Foundations and Applications, Faculty of Exact Sciences, University of El Oued, 39000, El Oued, Algeria Oued, 39000, El Oued, Algeria. | ||
| 2Department Mathematics, University of El Oued, Algeria | ||
| تاریخ دریافت: 27 آبان 1402، تاریخ پذیرش: 27 دی 1403 | ||
| چکیده | ||
| This paper explores a category of evolutionary variational problems. The formulation takes the shape of a system, encompassing a hyperbolic variational inequality (representing the displacement field), parabolic inequalities (capturing damage fields), and a differential equation (depicting the adhesion field). We establish the existence of a unique weak solution to this problem. The proof relies on the use of time-dependent variational inequalities, parabolic inequalities, differential equations, and fixed points. As an illustrative application, we explore a frictional dynamic contact problem involving a viscoelastic material with noncoercive viscosity, long-term memory, damage, and adhesion, accompanied by subdifferential boundary conditions. | ||
| کلیدواژهها | ||
| Variational inequality؛ hyperbolic؛ damage؛ fixed point؛ differential equations | ||
| مراجع | ||
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[1] C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities: Applications to Free-Boundary Problems, John Wiley, Chichester, 1984.
[2] M. Campo, J.R. Fernández, W. Han, and M. Sofonea, A dynamic viscoelastic contact problem with normal compliance and damage, Finite Elem. Anal. Des. 42 (2005), no. 1, 1-24.
[3] N. Costea and A. Matei, Contact models leading to variational-hemivariational inequalities, J. Math. Anal. Appl. 386 (2012), no. 2, 647-660.
[4] I. Doghri, Mechanics of Deformable Solids, Springer, Berlin, 2000.
[5] A.D. Drozdov, Finite Elasticity and Viscoelasticity: A Course in the Nonlinear Mechanics of Solids, World Scientific, Singapore, 1996.
[6] C. Eck, J. Jarusek, and M. Krbec, Unilateral Contact Problems: Variational Methods and Existence Theorems, Pure and Applied Mathematics, vol. 270, Chapman/CRC Press, New York, 2005.
[7] M. Frémond and B. Nedjar, Damage in gradient of damage and principle of virtual work, Int. J. Solids Struct. 33 (1996), no. 8, 1083-1103.
[8] M. Frémond and B. Nedjar, Damage in concrete: The unilateral phenomenon, Nucl. Eng. Des. 155 (1995), no. 1-2, 323-335.
[9] M. Frémond, K.L. Kuttler, B. Nedjar, and M. Shillor, One-dimensional models of damage, Adv. Math. Sci. Appl. 8 (1998), no. 2, 541-570.
[10] W. Han and M. Sofonea, Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity, Studies in Advanced Mathematics, vol. 30, American Mathematical Society, Providence, RI, International Press, Somerville, MA, 2002.
[11] A. Hamidat and A. Aissaoui, A quasi-static contact problem with friction in electro viscoelasticity with long-term memory body with damage and thermal effects, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 2, 205-220.
[12] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and their Applications, Classics in Applied Mathematics, vol. 31, SIAM, Philadelphia, 2000.
[13] A.M. Khludnev and J. Sokolowski, Modelling and Control in Solid Mechanics, Birkhäuser, Basel, 1997.
[14] A. Matei, A variational approach via bipotentials for a class of frictional contact problems, Acta Appl. Math. 134 (2014), no. 1, 45-59.
[15] D. Maugis, Contact, Adhesion and Rupture of Elastic Solids, Springer-Verlag, Berlin, Heidelberg, 2000.
[16] S. Migórski, A. Ochal, and M. Sofonea, Nonlinear Inclusions and Hemivariational Inequalities: Models and Analysis of Contact Problems, Advances in Mechanics and Mathematics, vol. 26, Springer, New York, 2013.
[17] S. Migórski and J. Ogorzaly, A class of evolution variational inequalities with memory and its application to viscoelastic frictional contact problems, J. Math. Anal. Appl. 442 (2016), no. 2, 685-702.
[18] S. Migórski and S. Zeng, Noncoercive hyperbolic variational inequalities with applications to contact mechanics, J. Math. Anal. Appl. 455 (2017), no. 1, 619-637.
[19] M. Rochdi, M. Shillor, and M. Sofonea, Analysis of a quasistatic viscoelastic problem with friction and damage, Adv. Math. Sci. Appl. 10 (2002), no. 1, 173-189.
[20] E. Rabinowicz, Friction and Wear of Materials, 2nd ed., John Wiley, New York, 1995.
[21] M. Sofonea, N. Renon, and M. Shillor, Stress formulation for frictionless contact of an elastic-perfectly-plastic body, Appl. Anal. 83 (2004), no. 11, 1157-1170.
[22] M. Sofonea, W. Han, and M. Shillor, Analysis and Approximations of Contact Problems with Adhesion or Damage, Pure and Applied Mathematics, Chapman Hall/CRC Press, Boca Raton, FL, 2006.
[23] R. Temam and A. Miranville, Mathematical Modeling in Continuum Mechanics, Cambridge University Press, Cambridge, 2001.
[24] B.I. Wohlmuth and R.H. Krause, Monotone multigrid methods on nonmatching grids for nonlinear multibody contact problems, SIAM J. Sci. Comput. 25 (2003), no. 1, 324–347.
[25] P. Wriggers and P.D. Panagiotopoulos (Eds.), New Developments in Contact Problems, Springer-Verlag, Wien and New York, 1999. | ||
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آمار تعداد مشاهده مقاله: 26 تعداد دریافت فایل اصل مقاله: 40 |
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