Engineering shapes on demand: tunable helical ribbons

The helix angle, chirality, and radius of helical ribbons are predicted with a comprehensive, three-dimensional analysis that incorporates elasticity, differential geometry, and variational principles. In many biological and engineered systems, ribbon helicity is commonplace and may be driven by surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. Unless coincident with the principle geometric axes of the ribbon, these anisotropies will lead to spontaneous, three-dimensional helical deformations. Analytical, closed-form ribbon shape predictions are validated with table-top experiments. More generally, our approach can be applied to develop materials and systems with tunable helical geometries.

This research work, Tunable Helical Ribbons, is published by Appl. Phys. Lett. 98, 011906 (2011); doi:10.1063/1.3530441.

A companion paper, Continuum Elasticity Theory Approach for Spontaneous Bending and Helicity of Ribbons Induced by Mechanical Anisotropy, has been submitted to J. Mech. Phys. Solids.