[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14317/jami.2021.813

A CONVERGENCE RESULTS FOR ANTIPLANE CONTACT PROBLEM WITH TOTAL SLIP RATE DEPENDENT FRICTION

AMMAR, DERBAZI (Faculty of Mathematics and Informatics, Department of Mathematics, University Mohamed)

Publication Information

Journal of applied mathematics & informatics / v.39, no.5_6, 2021 , pp. 813-823 More about this Journal

Abstract

In this work, we present the classical formulation for the antiplane problem of a eletro-viscoelastic materialswith total sliprate dependent friction and write the corresponding variational formulation. In the second step, we prove that the solution converges to the solution of the corresponding electro-elastic problem as the viscosity converges to zero.

Keywords

Antiplane shear deformation; contact process; electro-viscoelastic material; total slip rate dependent friction law;

Citations & Related Records

Reference

1	A. Borrelli, C.O. Horgan and M.C. Patria, Saint-Venant's principle for antiplane shear deformations of linear piezoelectic materials, SIAM J. Appl. Math. 62 (2002), 2027-2044. DOI
2	H. Brezis, Problemes unilateraux, J. Math. Pures Appl. 51 (1972), 1-168.
3	M. Campillo and I.R. Ionescu, Initiation of antiplane shear instability under slip dependent friction, Journal of Geophysical Research 102 (1997), 363-371. DOI
4	M. Dalah, Analysis of a Electro-Viscoelastic Antiplane Contact Problem With Total Slip-Rate Dependent Friction, Electronic. J. Differential Equations 2009 (2009), 1-16.
5	M. Dalah and F.L. Rahmani, Study and analysis of an antiplane electro-elastic contact problem with Tresca friction law, I.J.R.R.A.S. 12 (2012), 1-14.
6	A. Derbazi, M. Dalah and A. Megrous, The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory, Applications of Mathematics 61 (2016), 339-358. DOI
7	G. Duvaut and J.L. Lions, Inequalities in Mechanics and Physics, Springer-Verlag, Berlin, 1976.
8	K. Fernane and M. Dalah, A. Ayadi, Existence and uniqueness solution of a quasistatic electro-elastic antiplane contact problem with Tresca friction law, Applied Sciences 14 (2012), 45-59.
9	A. Matei and T.V. Hoarau-Mantel, Problemes antiplans de contact avec frottement pour des materiaux viscoelastiques a memoire longue, Annals of University of Craiova, Math. Comp. Sci. Ser. 32 (2005), 200-206.
10	A. Matei, V.V. Motreanu and M. Sofonea, A Quasistatic Antiplane Contact Problem With Slip Dependent Friction, Advances in Nonlinear Variational Inequalities 4 (2001), 1-21.
11	A. Megrous, A. Derbazi and M. Dalah, Existence and uniqueness of the weak solution for a contact problem, J. Nonlinear Sci. Appl. 9 (2016), 186-199. DOI
12	M. Sofonea, M. Dalah and A. Ayadi, Analysis of an antiplane electro-elastic contact problem, Adv. Math. Sci. Appl. 17 (2007), 385-400.