Tuning of Multi-stability Profile and Transition Sequence of Stacked Miura-Origami Metamaterials

Multi-stable origami structures and metamaterials possess unique advantages and could exhibit multiple stable three-dimensional configurations,which have attracted widespread research interest and held promise for applications in many fields.Although a great deal of attention has been paid to the design and application of multi-stable origami structures,less knowledge is available about the transition sequence among different stable configurations,especially in terms of the fundamental mechanism and the tuning method.To fill this gap,with the multi-stable dual-cell stacked Miura-ori chain as a platform,this paper explores the rules that govern the configuration transition and proposes effective methods for tuning the transition sequence.Specifically,by correlating the energy evolution,the transition paths,and the associated force-displace-ment profiles,we find that the critical extension/compression forces of the component cells play a critical role in governing the transition sequence.Accordingly,we summarize the rules for predicting the transition sequence:the component cell that first reaches the critical force during quasi-static extension or compression will be the first to undergo a configuration switch.Based on these findings,two methods,i.e.,a design method based on crease-stiffness assignment and an online method based on internal pressure regulation,are proposed to tune the stability profile and the transition sequence of the multi-stable origami structure.The crease-stiffness design approach,although effective,cannot be employed for online tuning once the prototype has been fabricated.The pressure-based approach,on the other hand,has been shown experimentally to be effective in adjusting the constitutive force-displacement profiles of the component cells and,in turn,tuning the transition sequence according to the summarized rules.The results of this study will advance the state of the art of origami mechanics and promote the engineering applications of multi-stable origami metamaterials.