Modelling Regular Article

The European Physical Journal Special Topics

, Volume 193, Issue 1, pp 133-160

First online:

Creep, relaxation and viscosity properties for basic fractional models in rheology

  • F. MainardiAffiliated withDepartment of Physics, University of Bologna Email author 
  • , G. SpadaAffiliated withDipartimento di Scienze di Base e Fondamenti, University of Urbino

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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.