Abstract
A constitutive equation for viscoelastic behavior containing time derivatives of stress and strain to fractional order is obtained from a fractal rheological model. Equivalence between tree and ladder fractal models at long times is demonstrated. The fractional differential equation is shown to be equivalent to ordinary differential formulations in the case of a simple power-law response; the adequacy of such formulations to describe non-linearity has been demonstrated previously. The model gives a good description of viscoelastic behavior under all stress modes and will be extended in future to include aging effects.
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Heymans, N., Bauwens, J.C. Fractal rheological models and fractional differential equations for viscoelastic behavior. Rheola Acta 33, 210–219 (1994). https://doi.org/10.1007/BF00437306
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DOI: https://doi.org/10.1007/BF00437306