Designing Shape Transitions in Elastic Structures

Many biological and engineered systems, from the Venus flytrap to mechanical metamaterials, exploit elastic instabilities and snap-through transitions to achieve a targeted function. Elastic strips, that buckle into one of two stable equilibrium states and snap from one state to the other as that state becomes unstable or suddenly disappears, have emerged as canonical systems for analyzing shape transitions. Here, we review recent advances that explain how geometric symmetries and symmetry-breaking mechanisms govern shape transitions in boundary-actuated elastic strips and provide universal rules for predicting or designing such transitions. We highlight the opportunities that this geometric understanding offers to emerging research areas, such as multi-functional metamaterials, morphological computing, and mechanical intelligence.