Generation of perversions in fibers with intrinsic curvature

If a fiber is stretched, abraded on one side, and then gradually relaxed, it will deform into a helix. If the two ends are restrained from rotating during the relaxation, it will form two helical segments of opposite chirality separated by a perversion. Here we investigate the properties of the perversion using a finite-element solution, and show that an excellent approximation to both the shape and the associated strain energy can be obtained using a simple Rayleigh-Ritz approximation. The perversion deviates from the adjacent helices only in a relatively small region, which suggests the possibility of approximating more complex geometries by treating perversions as point defects. Energetically, perversions are predicted only when they are 'geometrically necessary' because of the end restraint against rotation, but this energy differential is small when the fiber is almost straight and additional perversions can be generated by small perturbations. Some of these may approach and annihilate each other in pairs as the fiber is relaxed, but in other cases the additional perversions persist during unloading, despite the increased energy differential. (C) 2020 Elsevier Ltd. All rights reserved.