Spontaneous and Deterministic Three-Dimensional Curling of Pre-Strained Elastomeric Bi-Strips

Abstract

Three dimensional curls (“hemi-helices”) consisting of multiple, periodic and alternating helical sections of opposite chiralities, separated by perversions, are one of a variety of complex shapes that can be produced by a simple generic process consisting of pre-straining one elastomeric strip, joining it side-by-side to another and then releasing the bi-strip. The initial wavelength of the hemi-helix and the number of perversions are determined by the strip cross-section, the constitutive behavior of the elastomer and the value of the pre-strain. The hemi-helix has no net twist. Topologically, the perversions separate regions of the hemi-helix deforming principally by bending from those where twisting dominates.