Abstract: | Ordered mechanical systems typically have one or only a few stable rest configurations, and hence are not considered useful for encoding memory. Multistable and history-dependent responses usually emerge from quenched disorder, for example in amorphous solids or crumpled sheets. In contrast, due to geometric frustration, periodic magnetic systems can espouse an extensive manifold of quasi-degenerate configurations. Inspired by the topological structure of frustrated artificial spin ices, we introduce an approach to design ordered, periodic mechanical metamaterials that exhibit an extensive set of spatially disordered states. Our mechanical systems encompass continuous degrees of freedom, and are hence richer than their magnetic counterparts. We show how such systems exhibit history-dependent and non-Abelain responses, as their state may depend on the order in which external manipulations were applied. Thus, multistability and potential to store complex memory emerge from geometric frustration in ordered mechanical lattices that create their own disorder. |