Creep, relaxation and viscosity properties for basic fractional models in rheology
By Francesco Mainardi, Giorgio Spada. 2011
483 citations recorded by the source corpus.
Abstract.The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep, relaxation and viscosity properties are considered. The basic models are those that generalize via derivatives of fractional order the classical mechanical models characterized by two, three and four parameters, that we refer to as Kelvin–Voigt, Maxwell, Zener, anti–Zener and Burgers. For each fractional model we provide plots of the creep compliance, relaxation modulus and effective viscosity in non dimensional form in terms of a suitable time scale for different values of the order of fractional derivative. We also discuss the role of the order of fractional derivative in modifying the properties of the classical models.
Subfields: Biomedical Engineering, Fluid Flow and Transfer Processes, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/43c232bdc695529dff7ea1efc9184d3086cfa64a
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In Biomedical Engineering
In Fluid Flow and Transfer Processes
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Citations in the corpus
- Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems (2016, background): “, RiemannLiouville and Caputo FDs were considered to describe the anomalous relaxation [2,5,8,9,10].”
- Fractional viscoelastic models for power-law materials. (2020, background): “Such models are often referred to as generalised viscoelastic models and they have been mathematically characterized in the past [94, 95, 110].”