Generalized Kelvin–Voigt Creep Model in Fractal Space–Time

Eduardo Reyes de Luna, Andriy Kryvko, Juan B. Pascual-Francisco, Ignacio Hernández and Didier Samayoa ()
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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

Mathematics, 2024, vol. 12, issue 19, 1-13

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.

Keywords: fractal creep; viscoelastic materials; fractal continuum derivative; Kelvin–Voigt creep equation; Hausdorff dimension; chemical dimension (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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