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Generalized Kelvin–Voigt Creep Model in Fractal Space–Time

Author

Listed:
  • Eduardo Reyes de Luna

    (School of Engineering and Sciences, Tecnologico de Monterrey, Av. Carlos Lazo 100, Santa Fe, La Loma, Mexico City 01389, Mexico)

  • Andriy Kryvko

    (Instituto Politécnico Nacional, SEPI-ESIME Zacatenco, Unidad Profesional Adolfo López Mateos, Mexico City 07738, Mexico)

  • Juan B. Pascual-Francisco

    (Departamento de Mecatrónica, Universidad Politécnica de Pachuca, Carretera Pachuca-Cd. Sahagún Km. 20, Ex-Hacienda de Santa Barbara, Zempoala 43830, Mexico)

  • Ignacio Hernández

    (Instituto Politécnico Nacional, SEPI-ESIME Zacatenco, Unidad Profesional Adolfo López Mateos, Mexico City 07738, Mexico)

  • Didier Samayoa

    (Instituto Politécnico Nacional, SEPI-ESIME Zacatenco, Unidad Profesional Adolfo López Mateos, Mexico City 07738, Mexico)

Abstract

In this paper, we study the creep phenomena for self-similar models of viscoelastic materials and derive a generalization of the Kelvin–Voigt model in the framework of fractal continuum calculus. Creep compliance for the Kelvin–Voigt model is extended to fractal manifolds through local fractal-continuum differential operators. Generalized fractal creep compliance is obtained, taking into account the intrinsic time τ and the fractal dimension of time-scale β . The model obtained is validated with experimental data obtained for resin samples with the fractal structure of a Sierpinski carpet and experimental data on rock salt. Comparisons of the model predictions with the experimental data are presented as the curves of slow continuous deformations.

Suggested Citation

  • Eduardo Reyes de Luna & Andriy Kryvko & Juan B. Pascual-Francisco & Ignacio Hernández & Didier Samayoa, 2024. "Generalized Kelvin–Voigt Creep Model in Fractal Space–Time," Mathematics, MDPI, vol. 12(19), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3099-:d:1491943
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    References listed on IDEAS

    as
    1. Khalili Golmankhaneh, Alireza & Ontiveros, Lilián Aurora Ochoa, 2023. "Fractal calculus approach to diffusion on fractal combs," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Alexander S. Balankin & Juliã N Patiã‘O Ortiz & Miguel Patiã‘O Ortiz, 2022. "Inherent Features Of Fractal Sets And Key Attributes Of Fractal Models," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-23, June.
    3. Didier Samayoa & Alexandro Alcántara & Helvio Mollinedo & Francisco Javier Barrera-Lao & Christopher René Torres-SanMiguel, 2023. "Fractal Continuum Mapping Applied to Timoshenko Beams," Mathematics, MDPI, vol. 11(16), pages 1-12, August.
    4. Balankin, Alexander S. & Mena, Baltasar, 2023. "Vector differential operators in a fractional dimensional space, on fractals, and in fractal continua," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    5. Garra, Roberto & Mainardi, Francesco & Spada, Giorgio, 2017. "A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 333-338.
    6. Sara S. Alzaid & Ajay Kumar & Sunil Kumar & Badr Saad T. Alkahtani, 2023. "Chaotic Behavior Of Financial Dynamical System With Generalized Fractional Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-20.
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