“Controlled” geometric frustration leveraging local bistabililty in structural systems

Geometric frustration arises when a lattice system cannot simultaneously minimize all of its local interaction energies due to constraints, thus leading to degenerate and multiple disordered ground state configurations. Harnessing the ensuing multiple phase states for practical applications is a difficult controls problem due to the strong tendency for disorder, thus limiting the utility of these systems. Here, we present theoretical and experimental analyses of an archetypical lattice system for achieving “controlled” geometric frustration. The lattice features locally bistable dome units which upon inversion introduce prestress in the system. The patterning constrains the minimization of the interaction energies between neighboring inverted units and leads to geometric frustration that uniquely manifests in the form of hierarchical multistability i.e. multiple global states emerge for a given local inversion pattern. We further show that any desired frustrated global state can be achieved on demand by controlling the history of dome inversion, thus allowing for a simplified controls problem. This analysis essentially serves as a blueprint for leveraging geometric frustration for enabling mechanical computing platforms and programmable metamaterials.