Fractional viscoelastic models for power-law materials

Bonfanti, A and Kaplan, JL and Charras, G and Kabla, AJ Fractional viscoelastic models for power-law materials. Soft Matter 16:6002-6020 (2020). (Unpublished)

Abstract

Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad distribution of time-scales present in their complex internal structure. A promising tool to accurately describe the rheological behaviour of soft materials is fractional calculus. However, its use in the scientific community remains limited due to the unusual notation and non-trivial properties of fractional operators. This review aims to provide a clear and accessible description of fractional viscoelastic models for a broad audience, and to demonstrate the ability of these models to deliver a unified approach for the characterisation of power-law materials. The use of a consistent framework for the analysis of rheological data would help classify the empirical behaviours of soft and biological materials, and better understand their response.