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 - <p style="text-align: justify;">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.</p>