A Geometrically Exact Spectral Method for Elastohydrodynamics of Cosserat Rods

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• Mingjia Yan (University of Cambridge)
• Thursday 11 September 2025, 15:15-15:20
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TGM150 - 9th Edwards Symposium – Frontiers in Statistical Physics and Soft Matter

Slender structures are ubiquitous in biological and engineered systems, from bacterial flagella to soft robotic arms. The Cosserat rod provides a mathematical framework for slender bodies that can bend, twist, stretch and shear across multiple length scales. In viscous fluid environments at low Reynolds numbers, inertial effects become negligible, and hydrodynamic forces are well approximated by Stokes friction. We demonstrate that the resulting elastohydrodynamic equations of motion, when formulated using Cartan’s method of moving frames, possess the structure of a geometric field theory in which the configuration field takes values in SE(3) , the Lie group of rigid body motions. We present four different representations, namely, vectorial, moving frame, Lie group, and differential form formalisms, of the kinematics, dynamics and constitutive law of the Cosserat rod. Then, a spectral collocation method using Julia is exploited to numerically integrate the coordinatised equations of motion as an Initial-Boundary-Value problem (IBVP), where the local coordinates are specified by 2D translations and rotations. This IBVP is solved as a Differential-Algebraic Equations (DAEs), in which the boundary conditions are imposed as algebraic constraints. Finally, we show that the simulations of a clamped-free Cosserat rod exhibit the expected behaviours. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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