Lee, M. E. M. and Ockendon, H. (2005) A continuum model for entangled fibres. European Journal of Applied Mathematics, 16 (2). pp. 145160.

PDF
596kB 
Official URL: http://dx.doi.org/10.1017/S0956792505006170
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 fibrefibre 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 shearrates. 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 
Repository Staff Only: item control page