Shaping dynamical folding and misfolding pathways in mechanical metamaterials

Abstract: The design of desired behaviors in mechanical metamaterials has produced remarkable advances but has generally neglected two aspects - the inevitable presence of undesired behaviors and the role of dynamics in avoiding such behaviors. Inspired by similar hurdles in molecular self-assembly and protein folding, we derive design principles to shape dynamical folding and misfolding pathways in disordered mechanical systems. We show that such pathways, i.e., sequences of states traversed at a finite rate, are determined by the bifurcation structure of configuration space which, in turn, can be tuned using imperfections such as stiff joints. We apply these ideas to completely eliminate the exponentially many ways of misfolding a self-folding sheet by making some creases stiffer than others. Our approach also shows how folding at different rates can controllably target different desired behaviors.