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<p>This work deals with the variational study between dielectric medium and a rigid and insulating obstacle, under the constraints of non-penetration. The interactions of the material is governed by fractional electro-viscoelastic fundamental laws that incorporate linear electrical stress-displacement coupling and mechanical effects. Interface conditions are modeled using inequalities that capture both mechanical contact and perfect dielectric assumptions. To prove that there exists a solution, we use a variational framework that incorporates a Rothe temporal discretization method. Then we regularize the lateral conditions by introducing a penalization scheme. The analysis uses compactness arguments in fractional function spaces appropriately to Handle the behavior of the solution when the penalty variable reaches 0.</p>

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Variational Analysis of Unilateral Contact Problem Governed by Fractional Constitutive Law

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月10日

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  • Leila Ait Kaki,
  • Mohammed S. Abdo,
  • Khaled Aldwoah,
  • Arafa Dawood,
  • L. M. Abdalgadir

摘要

This work deals with the variational study between dielectric medium and a rigid and insulating obstacle, under the constraints of non-penetration. The interactions of the material is governed by fractional electro-viscoelastic fundamental laws that incorporate linear electrical stress-displacement coupling and mechanical effects. Interface conditions are modeled using inequalities that capture both mechanical contact and perfect dielectric assumptions. To prove that there exists a solution, we use a variational framework that incorporates a Rothe temporal discretization method. Then we regularize the lateral conditions by introducing a penalization scheme. The analysis uses compactness arguments in fractional function spaces appropriately to Handle the behavior of the solution when the penalty variable reaches 0.