European Journal of Applied Mathematics

Table of Contents - 2005 - Volume 16, Issue 02  


A continuum model for entangled fibres

M. E. M. LEE a1 and H. OCKENDON a2
a1 School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK email: lee@soton.ac.uk
a2 OCIAM, Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, UK

Article author query
lee me   [Google Scholar] 
ockendon h   [Google Scholar] 
 

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.

(Received December 23 2004)
(Revised February 9 2005)