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<p>This work studies a mathematical model involving a dynamic contact between two elasto-viscoplastic piezoelectric bodies with damage. The contact is modeled on a combination of a normal compliance and a normal damped response law associated with friction. We derive a variational formulation of the problem and we prove the existence and uniqueness result of the weak solution. The proof is based on the classical existence and uniqueness result for parabolic inequalities, differential equations and fixed-point arguments.</p>
<p>This paper examines a friction problem between two piezoelectric bodies that are elastic- viscoplastic. The study uses both numerical and analytical methods. The contact surface is assumed to have a thin layer of lubricant, and a damped response contact condition is considered. The problem also takes into account electrical and frictional effects. The paper proves the existence of a unique weak solution to the problem by using variational inequalities and a fixed point argument. Additionally, a fully discrete approximation is investigated using the Euler scheme and finite element method for the spatial variable and time derivatives. Error estimates are then calculated, leading to convergence results under certain regularity conditions.</p>
</abstract>

This work studies a mathematical model involving a dynamic contact between two elasto-viscoplastic piezoelectric bodies with damage. The contact is modeled on a combination of a normal compliance and a normal damped response law associated with friction. We derive a variational formulation of the problem and we prove the existence and uniqueness result of the weak solution. The proof is based on the classical existence and uniqueness result for parabolic inequalities, differential equations and fixed-point arguments.
This paper examines a friction problem between two piezoelectric bodies that are elastic- viscoplastic. The study uses both numerical and analytical methods. The contact surface is assumed to have a thin layer of lubricant, and a damped response contact condition is considered. The problem also takes into account electrical and frictional effects. The paper proves the existence of a unique weak solution to the problem by using variational inequalities and a fixed point argument. Additionally, a fully discrete approximation is investigated using the Euler scheme and finite element method for the spatial variable and time derivatives. Error estimates are then calculated, leading to convergence results under certain regularity conditions.

Variational and numerical analysis of a dynamic elasto-viscoplastic piezoelectric frictional contact problem

Kasdi Merbah University Department of Mathematics

University of El-Oued Department of Mathematics

General Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

This work studies a mathematical model involving a dynamic contact between two elasto-viscoplastic piezoelectric bodies with damage. The contact is modeled on...

Variational and numerical analysis of a dynamic elasto-viscoplastic piezoelectric frictional contact problem

Publicado en línea: 07 mar 2024

Páginas: 51 - 79

Recibido: 23 sept 2023

Aceptado: 11 dic 2023

DOI: https://doi.org/10.2478/gm-2023-0012

Palabras clave
elastic-viscoplastic piezoelectric materials, frictional contact, evolution equations, fixed point, error estimates

© 2023 Maiza Laid et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Variational and numerical analysis of a dynamic elasto-viscoplastic piezoelectric frictional contact problem

Publicado en línea: 07 mar 2024

Páginas: 51 - 79

Recibido: 23 sept 2023

Aceptado: 11 dic 2023

DOI: https://doi.org/10.2478/gm-2023-0012

Palabras claveelastic-viscoplastic piezoelectric materials, frictional contact, evolution equations, fixed point, error estimates

© 2023 Maiza Laid et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Palabras clave
elastic-viscoplastic piezoelectric materials, frictional contact, evolution equations, fixed point, error estimates