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According to Sadykova 1972, the Poisson ratio express the change in the volume of a solid undergoing deformation. For cotton it would be how the Cotton fiber volume will change when apply a tensile force in X direction and how much changes will happen in the lateral direction. That is Passion ratio, I did not find anyone how calculated that for cotton fibres but there are some studies for the woven fabrics or yarns. If I am not mistaken some Instron testers can calculate that for your sample directly.

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Q: What is the Poisson ratio of cotton?
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