The twisting mechanics of undulated ribbons: theory and application to morphing structures

Stress localization at compliant hinges and flexures makes it challenging to design durable, low-part-count, load bearing systems that can undergo complex and reversible changes in shape. Here, we investigate the use of bulk metallic glass (BMG) ribbons that have been thermoformed into twisted, stress-free configurations as building blocks for shape-changing structures. The post-twisting helicoidal shape allows the ribbons to have preferred bending directions that vary throughout their length. A boundary undulation allows to introduce a bias and to make some bending directions more favorable. The result is that twisted undulated ribbons behave as structural elements with multi-directional compliant joints. We join multiple ribbons to create deployable systems with complex morphing attributes enabled by the intrinsic chirality of the building blocks. The design of our structures is informed by an investigation of non-rectangular ribbon mechanics through a combination of numerical simulations, an analytical model based on a geometrically nonlinear plate theory and torsional experiments.