The compressional mechanism of a random fiber assembly is analyzed by an energy method. An infinitesimal fiber segment, which is bounded by two neighboring contact points, is chosen as the unit bending element. The geometry of this element is characterized by its arc length, curvature, and orientation. The change in bending energy of each fiber segment due to the compression of the assembly is derived in terms of the compressional strain and the Poisson's ratio of the assembly. The summation of each energy contribution is done using a continuous joint probability density function of the length and orientation of the segments.
Get full access to this article
View all access options for this article.
References
1.
CarnabyG. A., The Compression of Fibrous Assemblies with Applications to Yarn Mechanics, in “Mechanics of Flexible Fibre Assemblies,”HearleJ. W. S.ThwaitesJ. J.AmirbayatJ., Eds., Sijthoff and Noordhoff, Alphen aan den Rijn, The Netherlands, 1980, pp. 99–112.
2.
CarnabyG. A.CuriskisJ. I., The Tangent Compliance of Staple-fibre Bundles in Tension, J. Textile Inst.78, 293–305 (1987).
3.
CarnabyG. A.PanN., Theory of the Compression Hysteresis of Fibrous Assemblies, Textile Res. J.59, 275–284 (1989).
4.
CuriskisJ. I.CarnabyG. A., Continuum Mechanics of the Fiber Bundle, Textile Res. J.55, 334–344 (1985).
5.
KallmesO.CorteH., The Structure of Paper, I: The Statistical Geometry of an Ideal Two-dimensional Fibre Network, Tappi43, 737–752 (1960).
6.
KomoriT.MakishimaK., Numbers of Fiber-to-fiber Contacts in General Fiber Assemblies, Textile Res. J.47, 13–17 (1977).
7.
LeeD. H., Initial Compressional Behaviour of Fibre Assembly (in Korean), Doctoral thesis, Seoul National University, Seoul, Korea, 1985.
8.
LeeD. H.CarnabyG. A.CarrA. J.MossP. J., A Review of Current Micromechanical Models of the Unit Fibrous Cell, WRONZ Communication no. CI 13, 1990.
9.
LeeD. H.LeeJ. K., Initial Compressional Behaviour of Fibre Assembly, in “Objective Measurement: Applications to Product Design and Process Control,”KawabataS.PostleR.NiwaM., Eds., Textile Machinery Society of Japan, Osaka, 1985, pp. 613–622.
10.
PanN.CarnabyG. A., The Initial Shear Modulus of a Unit Cell of Wool Fibres, WRONZ Communication no. C106, 1988.
11.
PanN.CarnabyG. A., Theory of the Shear Deformation of Fibrous Assemblies, Textile Res. J.59, 285–292 (1989).
12.
van WykC. M., Note on the Compressibility of Wool, J. Textile Inst.37, T285–T292 (1946).
13.
van WykC. M., A Study of the Compressibility of Wool, with Special Reference to South African Merino Wool, Onderstepoort J. Vet. Sci. Anim. Ind.21, 99–226 (1946).
