We study the compression of bundles of aligned macroscopic fibers with intrinsic shape disorder, as found in human hair and in many other natural and man-made systems. We show by a combination of experiments, numerical simulations and theory how the statistical properties of the shapes of the fibers control the collective mechanical behaviour of the bundles. This work paves the way for designing aligned fibrous matter with purposed-designed properties from large numbers of individual strands of selected geometry and rigidity.
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