A multi-stable metamaterial design method (MSMDM) based on a bistable chiral structure

Abstract

The design of multistable metamaterials has predominantly relied on trial-and-error strategies and geometry-specific optimization, limiting systematic exploration of design spaces. Despite numerous reported architectures, unified approaches for the generation and classification of planar and spatial multistable systems remain underdeveloped. This work introduces the Multistable Metamaterial Design Method (MSMDM), a topology-driven generative framework for the systematic discovery, classification, and nomenclature of multistable structures. Starting from a fundamental chiral bistable seed (Z_B) and its spatial extension (Z_3B), the method employs a discrete set of seven topological transformations to reconstruct existing designs and generate new multistable families. A key contribution is the definition of the superchirality order χ, a compact descriptor that enables consistent characterization of chirality across dimensions and captures its evolution during structural transformations. The MSMDM is demonstrated to reproduce structures that exhibit a broad spectrum of mechanical responses, including monostable, neutrally stable, and countersnapping behaviors exhibiting contraction under extension. By defining unit cells through a Voronoi-based formalism, the framework ensures compatibility with scalable planar and spatial tessellations. Overall, MSMDM establishes a unified design language that decouples topological generation from mechanical optimization, providing a robust foundation for application-driven development in areas such as soft robotics, deployable systems, and energy absorption.