Volume 7, Issue 2
Analysis of a Contact Problem Modeled by Hemivariational Inequalities in Thermo-Piezoelectricity

Mohammed Alaoui, El-Hassan Essoufi, Abdelhafid Ouaanabi & Bouallala Mustapha

J. Nonl. Mod. Anal., 7 (2025), pp. 739-763.

Published online: 2025-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

We study a quasistatic contact problem from both variational and numerical perspectives, focusing on a thermo-piezoelectric body interacting with an electrically and thermally rigid foundation. The contact is modeled with a normal damped response and unilateral constraint for the velocity field, associated with a total slip-dependent version of Coulomb’s law of dry friction. The electrical and thermal conditions on the contact surface are described by Clarke’s subdifferential boundary conditions. We formulate the problem’s weak form as a system combining a variational-hemivariational inequality with two hemivariational inequalities. Utilizing recent results in the theory of hemivariational inequalities, along with the fixed point method, we demonstrate the existence and uniqueness of the weak solution. Furthermore, we examine a fully discrete scheme for the problem employing the finite element method, and we establish error estimates for the approximate solutions.

  • AMS Subject Headings

74Fxx, 74M10, 58J20, 74M15, 47J22, 74S05

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COPYRIGHT: © Global Science Press

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@Article{JNMA-7-739, author = {Alaoui , MohammedEssoufi , El-HassanOuaanabi , Abdelhafid and Mustapha , Bouallala}, title = {Analysis of a Contact Problem Modeled by Hemivariational Inequalities in Thermo-Piezoelectricity}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {2}, pages = {739--763}, abstract = {

We study a quasistatic contact problem from both variational and numerical perspectives, focusing on a thermo-piezoelectric body interacting with an electrically and thermally rigid foundation. The contact is modeled with a normal damped response and unilateral constraint for the velocity field, associated with a total slip-dependent version of Coulomb’s law of dry friction. The electrical and thermal conditions on the contact surface are described by Clarke’s subdifferential boundary conditions. We formulate the problem’s weak form as a system combining a variational-hemivariational inequality with two hemivariational inequalities. Utilizing recent results in the theory of hemivariational inequalities, along with the fixed point method, we demonstrate the existence and uniqueness of the weak solution. Furthermore, we examine a fully discrete scheme for the problem employing the finite element method, and we establish error estimates for the approximate solutions.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.739}, url = {http://global-sci.org/intro/article_detail/jnma/24025.html} }
TY - JOUR T1 - Analysis of a Contact Problem Modeled by Hemivariational Inequalities in Thermo-Piezoelectricity AU - Alaoui , Mohammed AU - Essoufi , El-Hassan AU - Ouaanabi , Abdelhafid AU - Mustapha , Bouallala JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 739 EP - 763 PY - 2025 DA - 2025/04 SN - 7 DO - http://doi.org/10.12150/jnma.2025.739 UR - https://global-sci.org/intro/article_detail/jnma/24025.html KW - Thermo-piezoelectric materials, friction, hemivariational inequality, fixed point argument, finite element method. AB -

We study a quasistatic contact problem from both variational and numerical perspectives, focusing on a thermo-piezoelectric body interacting with an electrically and thermally rigid foundation. The contact is modeled with a normal damped response and unilateral constraint for the velocity field, associated with a total slip-dependent version of Coulomb’s law of dry friction. The electrical and thermal conditions on the contact surface are described by Clarke’s subdifferential boundary conditions. We formulate the problem’s weak form as a system combining a variational-hemivariational inequality with two hemivariational inequalities. Utilizing recent results in the theory of hemivariational inequalities, along with the fixed point method, we demonstrate the existence and uniqueness of the weak solution. Furthermore, we examine a fully discrete scheme for the problem employing the finite element method, and we establish error estimates for the approximate solutions.

Alaoui , MohammedEssoufi , El-HassanOuaanabi , Abdelhafid and Mustapha , Bouallala. (2025). Analysis of a Contact Problem Modeled by Hemivariational Inequalities in Thermo-Piezoelectricity. Journal of Nonlinear Modeling and Analysis. 7 (2). 739-763. doi:10.12150/jnma.2025.739
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