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<p>In this work, we explore a mathematical model that describes quasistatic, frictionless contact between a deformable body and a rigid foundation. The material behavior is characterized by a thermo-viscoelastic constitutive law incorporating a memory term within the model. The contact is characterized by a normal damped response, a unilateral constraint, and a memory term. We present the traditional statement of the issue and establish a variational formulation for the model. Afterward, we establish the weak solvability of the problem. Our analysis is based on the framework of evolutionary quasivariational inequalities and relies on a classical result concerning first-order evolution equations combined with a fixed-point argument. Finally, two-dimensional numerical examples are presented to show the behavior of the solution.</p>

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Analysis of a thermo-viscoelastic contact problem with normal damped response, unilateral constraint and memory term

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Mustapha Bouallala,
  • Youssef Ouafik,
  • Abdesadik Bendarag

摘要

In this work, we explore a mathematical model that describes quasistatic, frictionless contact between a deformable body and a rigid foundation. The material behavior is characterized by a thermo-viscoelastic constitutive law incorporating a memory term within the model. The contact is characterized by a normal damped response, a unilateral constraint, and a memory term. We present the traditional statement of the issue and establish a variational formulation for the model. Afterward, we establish the weak solvability of the problem. Our analysis is based on the framework of evolutionary quasivariational inequalities and relies on a classical result concerning first-order evolution equations combined with a fixed-point argument. Finally, two-dimensional numerical examples are presented to show the behavior of the solution.