Multi-step self-guided pathways for shape-changing metamaterials.

Multi-step pathways-which consist of a sequence of reconfigurations of a structure-are central to the functionality of various natural and artificial systems. Such pathways execute autonomously in self-guided processes such as protein folding1 and self-assembly2-5, but have previously required external control to execute in macroscale mechanical systems, provided by, for example, actuators in robotics6-9 or manual folding in origami8,10-12. Here we demonstrate shape-changing, macroscale mechanical metamaterials that undergo self-guided, multi-step reconfiguration in response to global uniform compression. We avoid the need for external control by using metamaterials that are made purely of passive components. The design of the metamaterials combines nonlinear mechanical elements with a multimodal architecture that enables a sequence of topological reconfigurations caused by the formation of internal self-contacts between the elements of the metamaterial. We realize the metamaterials by using computer-controlled water-jet cutting of flexible materials, and show that the multi-step pathway and final configuration can be controlled by rational design of the nonlinear mechanical elements. We also demonstrate that the self-contacts suppress errors in the pathway. Finally, we create hierarchical architectures to extend the number of distinct reconfiguration steps. Our work establishes general principles for designing mechanical pathways, opening up new avenues for self-folding media11,12, pluripotent materials9,13 and pliable devices14 in areas such as stretchable electronics and soft robotics15.