The Mathematical Institute, University of Oxford, Eprints Archive

A continuum model for entangled fibres

Lee, M. E. M. and Ockendon, H. (2005) A continuum model for entangled fibres. European Journal of Applied Mathematics, 16 (2). pp. 145-160.


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Motivated by the study of fibre dynamics in the carding machine, a continuum model for the motion of a medium composed of fibres is derived under the assumption that the dominant forces are due to fibre-fibre interactions and that the material is in tension. To characterise the material we include the averaged values of density and velocity and introduce variables to describe the mean direction, alignment and entanglement. We assume that the bulk stress of the material depends on the density, entanglement, degree of alignment, average direction and shear-rates. A kinematic equation for average direction and two proposed heuristic laws for the evolution of entanglement and degree of alignment are given to close the system. Extensional and shearing simulations are in good qualitative agreement with experimental results.

Item Type:Article
Subjects:H - N > Mechanics of deformable solids
O - Z > Partial differential equations
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:280
Deposited By: Gareth Wyn Jones
Deposited On:02 Oct 2006
Last Modified:29 May 2015 18:19

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