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A continuum model for entangled fibres

Published online by Cambridge University Press:  23 May 2005

M. E. M. LEE  and
H. OCKENDON
M. E. M. LEE
Affiliation:
School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK email: [email protected]
H. OCKENDON
Affiliation:
OCIAM, Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, UK
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Abstract

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.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 16 , Issue 2 , April 2005 , pp. 145 - 160
Copyright
2005 Cambridge University Press

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