This paper formulates, in concise style, the differential equations and the boundary conditions describing the deformed shape of a three-dimensional crimped fiber subjected to end loads; a more complete analysis may be found in [1] and [3]. Bending and twisting effects are taken into account, but stretching of the axis and the deformation due to cross shear are neglected. An example, for which an exact solution is possible, is included and a simple experiment, providing limited experimental confirmation, is reported.
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References
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ChicurelR., Dissertation, Princeton University (1959).
2.
ChicurelR.SuppigerE., “Load-Deflection Analysis of Fibers with Plane Crimp”, Textile Research J.30, 568–575 (1960).
3.
ChicurelR.SuppigerE., “Deformation of Elastic Filaments with Arbitrary Unstressed Configurations”, Z. Angew. Math. Phys.13, 58–76 (1962).
4.
HoldawayH. W., “A Helical Spring Model for the Uncrimping of Wool Fibers”, J. Textile Inst.47, T586–T602 (1956).
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LanczosC., “The Variational Principles of Mechanics”, Toronto, University of Toronto Press, 1949, pp. 57–60.
