Department Seminar Series

Modelling the mechanics of fractal and non-fractal fibre networks

2nd December 2025, 13:00 add to calenderELEC201, 2th Floor Lecture Theater EEE
David Head
University of Leeds

Abstract

Many natural and synthetic materials are composed in part of a connected network of slender elastic objects, such as the cellular cytoskeleton in mammalian cells, fibrinogen in blood clots, and cellulose in paper. These first two examples are protein networks, currently undergoing vigorous research as a class of biocompatible, biodegradable materials with almost unlimited controls to tailor bulk properties for target applications. However, this also presents a challenge, as it is not possible to empirically characterise all variations without guidance from modelling. In this talk, I will overview recent and outstanding problems in the modelling of fibre networks. Early simulations considered the static mechanical response of crosslinked elastic fibre networks, solved using a sparse iterature solver such as conjugate gradient, but more recently the role of the interstitial fluid, relevant to most applications, has been considered. By assuming steady state response under small-amplitude oscillatory shear, it is possible to derive a matrix equation that can be efficiently solved, generating smooth data over many orders of magnitude of frequency, and for regions of weak and strong coupling between the network and fluid to be clearly delineated. Then, motivated by experiments demonstrating protein hydrogels are fractal, the same methodology produces a clear power-law dependence of the mechanical response with frequency, and highlights the limitations of branched polymer network theories. I will finish with a summary of ongoing work, including fibrinogen (blood clot) modelling, and the potentially exciting new physics from allowing the network building blocks to dynamically unfold due to internal stresses.
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Biography

From a PhD in statistical physics, I went on a nomadic post-doctoral journey passing through Edinburgh, Amsterdam, Tokyo and Juelich (Germany) before settling down to a permanent position in the University of Leeds. During this time I have worked on a range of soft matter and biological physics systems, usually with an emphasis on model development and efficient numerical solutions, include large sparse matrix equations and particle-based simulation methods, for complex systems such as bacterial biofilms and biopolymer networks; the latter will be the focus of today's talk.

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