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<p>In this paper, we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect, in which the contact conditions are described by a Signorini’s condition and Coulomb’s friction law. We derive the variational form of the contact problem which is a mixed system formulated by variational inequalities and equalities. Then, we use standard results on mixed problems and the Banach fixed-point theorem to prove the existence and uniqueness of the solution to the contact problem. Moreover, we demonstrate the convergence of a penalty method for this contact problem under consideration. Finally, finite element method is applied to the penalty contact problem and a strong convergence theorem is obtained.</p>

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A class of nonlinear thermo-piezoelectric contact problem with Coulomb’s law: Existence, uniqueness and convergence

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Jinxia Cen,
  • Abdelhadi Hachlaf

摘要

In this paper, we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect, in which the contact conditions are described by a Signorini’s condition and Coulomb’s friction law. We derive the variational form of the contact problem which is a mixed system formulated by variational inequalities and equalities. Then, we use standard results on mixed problems and the Banach fixed-point theorem to prove the existence and uniqueness of the solution to the contact problem. Moreover, we demonstrate the convergence of a penalty method for this contact problem under consideration. Finally, finite element method is applied to the penalty contact problem and a strong convergence theorem is obtained.