Taming geometric frustration by leveraging structural elasticity

TL;DR

This paper introduces a continuum system with bistable units that can be controlled to manifest and study geometric frustration, providing a new approach to understanding and utilizing frustration in structural systems.

Contribution

The authors develop a controllable continuum model that encodes multiple frustrated states and demonstrates how to access them on-demand, advancing the understanding of geometric frustration.

Findings

Controlled activation of frustrated states via unit inversion.

Observation of microstructural evolution during frustration unfolding.

Blueprint for using structural systems in computation and optimization.

Abstract

Geometric frustration appears in a broad range of systems, generally emerging as disordered ground configurations, thereby impeding understanding of the phenomenon's underlying mechanics. We report on a continuum system featuring locally bistable units that allows for the controlled and self-sustained manifestation of macroscopic geometric frustration. The patterning of the units encodes a finite set of ordered ground configurations (spin-ice states) and a unique family of co-existing higher-order frustrated states (spin-liquid states), which are both activated upon unit inversion. We present a strategy for accessing any globally frustrated state on-demand by controlling the constitutive units' inversion sequence. This control strategy allows for observing the unfolding of geometric frustration as the microstructural features evolve due to the energy minimization of the constitutive units' interactions. More broadly, our model system offers a blueprint for "taming" macroscopic geometric frustration, enabling novel applications such as path-driven computation and solving optimisation problems using structural systems.