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A problem involving time-fractional contact with normal compliance and Tresca’s friction within the realm of electro-viscoelasticity

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  • Bouallala, Mustapha
  • Essoufi, EL-Hassan
  • Liao, Shanli

Abstract

This paper examines a fractional contact problem involving friction for an electro-viscoelastic body resting on a conductive foundation. The contact is characterized using the normal compliance condition, while friction behavior is modeled using Tresca’s law. The variational formulation is provided, and the existence of the weak solutions is proved. The proofs are based on the theory of monotone operator, fractional calculus analysis and fixed-point theorem. Additionally, we are committed to exploring numerical methods for solving the contact problem. This entails utilizing spatially semi-discrete and fully discrete finite elements along with discrete approximations of fractional derivatives. Moreover, we aim to provide error estimates for the solutions obtained through these approximations.

Suggested Citation

  • Bouallala, Mustapha & Essoufi, EL-Hassan & Liao, Shanli, 2024. "A problem involving time-fractional contact with normal compliance and Tresca’s friction within the realm of electro-viscoelasticity," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924010361
    DOI: 10.1016/j.chaos.2024.115484
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