In the previous paper, the yarn axis crimped in the fabric was assumed to be expressed by the following equation which contains an important parameter
n. Here
l is the length of a quarter of crimp measured along x-axis, which is the direction of tension and
a is its amplitude. This shape of the yarn axis is also applied to crimped fiber. Using the above equation, the strain energy
U of the crimped fiber is obtained. The deflection in the direction of the force is deduced from Castigliano's theorem. By expansion using binomial series, the initial resistance of the crimped fiber is obtained, but it is not useful for practical problems, as it is in too complicated form. Introducing
m, which depends upon
a,
l and
n, the practical equation of the initial resistance is obtained. These results are shown in equation (22). This theoretical equation was discussed by using the crimped model filament. The constant
EI for three model filaments with the same
EI but with various crimps was not constant when calculated from Van Wyk's theory, but it was constant from the author's theory.
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