Measurements on filaments

The filament s transverse isotropy implies that under compressive loading normal to the fibre axis the stresses in the transverse plane are identical in form to those for the compression of an isotropic cylinder and, provided that the length of the filament under compression is long compared with the width of the contact strip 2b, friction ensures that compression occurs under plane strain conditions. As = 0 only a normal stress acts along the filament axis, which can be found in terms of the normal stresses and oy, in the perpendicular plane, i.e. 

The stresses can therefore be obtained from the solution to the problem of compression of an isotropic cylinder, and the corresponding strains derived from 

Through an extension of Hertz s solution for the compression of an isotropic cylinder Ward was able to derive an analytical solution for the contact width 2b, of the form 

Further, it can be shown that the diametral compression u parallel to the direction of the applied load is [16] 

Thus measurement of the diametral expansion provides a method of determining 512, once 5ii has been derived from a measurement of the contact width. 

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Packer, H. L., and C. R. Thomas (1990). Morphological measurements on filamentous micro-organisms by fully automatic image analysis, Biotechnol. Bioeng., 35, 870-881. 

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