Modeling and Design of Non-Abelian Multistable Soft Metastructures

Morphing structures, soft materials, and metamaterials present new opportunities for mechanical computation, reduced control complexity, and shape programmability. Recently, incorporating mechanical instabilities into soft structures has gained interest due to their ability to exhibit multiple energy minima, path-dependent unit activation, or non-Abelian response, and the influence of local prestress on global shape configurations. As each unit cell can be reversibly inverted at a local scale, multiple stable shapes at a global scale can be achieved. These shapes are highly dependent on the unit geometry, inversion sequence, and number of units, which makes their behavior challenging to analyze and predict. Given this, simple yet robust models are needed to predict the final state of the structure efficiently, enabling faster analysis and inverse design. To address this, we present a lumped-element model that predicts the order-dependent deflections and final shape of soft structures based on unit count and geometric parameters. Our approach utilizes automatic relevance determination (ARD) regression, combined with numerical data, to derive simplified yet robust models for fast analysis and inverse design. This computationally efficient model allows exploration of the configuration space, enabling inverse co-design of soft structures by specifying desired target shapes. Furthermore, we examine the interaction between units to determine optimal strategies to leverage all these multiple states in applications such as soft robotics and mechanical computation. The co-design and optimal control enabled by our model opens a route for the fast design of multistable soft robots and shapes targeting soft metastructures.