Creep, Relaxation and Viscosity Properties for Basic Fractional Models in Rheology

TL;DR

This paper surveys viscoelastic models based on fractional calculus and analyzes their creep, relaxation, and viscosity properties, highlighting how fractional derivatives modify classical model behaviors.

Contribution

It provides a comprehensive survey of fractional viscoelastic models and analyzes their fundamental properties with detailed plots and discussions.

Findings

Fractional models generalize classical mechanical models.

The order of fractional derivatives significantly affects model properties.

Plots illustrate the impact of fractional order on viscoelastic behavior.

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.