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<p>This paper is devoted to a study of the numerical solution of thermo-viscoelastic model describing contact problem between the body and a rigid foundation which, is thermally conducting. The behavior of the material is described by the linear thermo-viscoelastic constitutive law of the Caputo type. The contact is modelled by the Signorini’s condition and the friction by the Coulomb law. Additionally, the thermal contact and the frictional heat generation are also addressed. The heat exchange coefficient takes into account the contact pressure. Our aim is to present a detailed description of the numerical modelling of the problem. To this end, we use an augmented Lagrangian method to approximate the constraints. A solution algorithm is discussed and implemented, and numerical simulations of the process are presented to show the impacts of the fractional parameter in thermo-viscoelastic medium for all considered variables.</p>

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Modeling and simulation of time-fractional derivative contact problem in thermo-viscoelasticity

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • Mustapha Bouallala,
  • EL-Hassan Essoufi,
  • Youssef Ouafik

摘要

This paper is devoted to a study of the numerical solution of thermo-viscoelastic model describing contact problem between the body and a rigid foundation which, is thermally conducting. The behavior of the material is described by the linear thermo-viscoelastic constitutive law of the Caputo type. The contact is modelled by the Signorini’s condition and the friction by the Coulomb law. Additionally, the thermal contact and the frictional heat generation are also addressed. The heat exchange coefficient takes into account the contact pressure. Our aim is to present a detailed description of the numerical modelling of the problem. To this end, we use an augmented Lagrangian method to approximate the constraints. A solution algorithm is discussed and implemented, and numerical simulations of the process are presented to show the impacts of the fractional parameter in thermo-viscoelastic medium for all considered variables.