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Cambridge Centre for Physical Biology

 

Fractional viscoelastic models for power-law materials

 

The mechanical response of soft materials, and in particular cells and tissues, exhibits a broad distribution of time-scales due to the complex structure and dynamics of these systems. This rich response is often associated with a characteristic power-law signature in the spectrum of the mechanical relaxation times and in the way stress relaxes or creep deformation progresses.

Fractional calculus, a branch of mathematics that extends the range of traditional differential operators, can be used to accurately capture and predict the rheological behaviour of such materials. We demonstrated in our earlier work [1] that a viscoelastic model making use of such techniques can characterise over a broad range of time scales the mechanical behaviour of a number of cells and tissues. Our recent review article [2] provides a clear and accessible description of fractional viscoelastic models for a broad audience and shows that these models can deliver a consistent approach for the characterisation of power-law materials. Such consistency in the analysis of rheological data would help classify the empirical behaviours of soft and biological materials, and ultimately better understand the physical origin of their response. 

To assist scientists with the use of these techniques, we developed a software library available in the public domain [3] which was used to produce the review figures as well as its annex which presents in detail the most relevant classes of fractional models.
 

 

 

[1] Bonfanti, A., Fouchard, J., Khalilgharibi, N., Charras, G., & Kabla, A. (2020). A unified rheological model for cells and cellularised materials. Royal Society Open Science, 7(1), 190920. https://doi.org/10.1098/rsos.190920 
[2] Bonfanti, A., Kaplan, J. L., Charras, G., & Kabla, A. (2020). Fractional viscoelastic models for power-law materials. Soft Matter, 16(26), 6002–6020. https://doi.org/10.1039/d0sm00354a
[3] Kaplan, J., Bonfanti, A., & Kabla, A. (2019). RHEOS.jl - A Julia Package for Rheology Data Analysis. Journal of Open Source Software, 4(41), 1700. https://doi.org/10.21105/joss.01700