Numerical analysis of a frictional contact problem for thermo-electro-elastic materials
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National School of Applied Sciences of Safi, Cadi Ayyad University, Safi, Morocco
Submission date: 2018-12-25
Final revision date: 2019-03-31
Acceptance date: 2019-11-29
Online publication date: 2020-07-15
Publication date: 2020-07-15
Corresponding author
Ouafik Youssef   

IRT, Université Cadi Ayyad, ENSA Safi, Route Sidi Bouzid, 46000, Safi, Morocco
Journal of Theoretical and Applied Mechanics 2020;58(3):673-683
A numerical method is presented for a mathematical model which describes the frictional contact between a thermo-electro-elastic body and a conductive foundation. The contact is described by Signorini’s conditions and Tresca’s friction law including electrical and ther- mal conductivity conditions. Our aim is to present a detailed description of the numerical modelling of the problem. To this end, we introduce a discrete scheme based on the finite element method. Under some regularity assumptions imposed on the true solution, optimal order error estimates are derived for the linear element solution. This theoretical result is illustrated numerically.
Alart P., Curnier A., 1988, A generalized Newton method for contact problems with friction, Journal of Theoretical and Applied Mechanics, 7, 6-82.
Baiz O., Benaissa H., El Moutawakil D., Fakhar R., 2018, Variational and numerical analysis of a static thermo-electro-elastic problem with friction, Mathematical Problems in Engineering, 2018, 1-16.
Barboteu M., Sofonea M., 2009, Modeling and analysis of the unilateral contact of a piezoelectric body with a conductive support, Journal of Mathematical Analysis and Applications, 358, 110-124.
Benaissa H., Essoufi E.-H., Fakhar R., 2015, Existence results for unilateral contact problem with friction of thermo-electro-elasticity, Applied Mathematics and Mechanics, 36, 911-926.
Benaissa H., Essoufi E.-H., Fakhar R., 2016, Analysis of a Signorini problem with nonlocal friction in thermo-piezoelectricity, Glasnik Matematiˇcki, 51, 391-411.
Ciarlet P.G., 1978, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam.
Essoufi E.-H., Fakhar R., Koko J., 2015, A decomposition method for a unilateral contact problem with Tresca friction arising in electro-elastostatics, Numerical Functional Analysis and Optimization, 36, 1533-1558.
Laursen T.A., 2002, Computational Contact and Impact Mechanics, Springer, Berlin, Germany.
Liu P., Yu T., Bui T.Q., Zhang C., Xu Y., Lim C.W., 2014, Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method, International Journal of Solids and Structures, 51, 2167-2182.
Renard Y., 2013, Generalized Newton’s methods for the approximation and resolution of frictional contact problems in elasticity, Computer Methods in Applied Mechanics and Engineering, 256, 38-55.
Shang F., Kuna M., Scherzer M., 2002, A finite element procedure for three-dimensional analyses of thermopiezoelectric structures in static applications, Technische Mechanik, 22, 235-243.
Sládek J., Sládek V., Staňák P., 2010, Analysis of thermo-piezoelectricity problems by meshless method, Acta Mechanica Slovaca, 14, 16-27.
Tiersten H.F., 1971, On the non linear equation of electro-thermo-elasticity, International Journal of Engineering Science, 9, 587-604.
Wriggers P., 2002, Computational Contact Mechanics, John Wiley & Sons, Chichester, UK Manuscript received.
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