Reduced order modeling of hierarchically multistable metastructures

Reconfigurable structures, soft materials, and metamaterials have introduced new opportunities for mechanical computation, control complexity reduction, and shape programmability. Recently, architecture materials composed of patterned arrays of bistable units have gained interest due to their capabilities of exhibiting multiple energy minima, unit activation path dependency, and influence of local prestress in its global shape. As each unit cell can be reversibly inverted at a local scale, multiple stable shapes at a global scale are achieved. These shapes are highly dependent on the unit geometry, inversion sequence, number of units, and unit spatial distribution, which makes their behavior challenging to analyze and predict. Given this, simpler yet robust models need to be utilized to predict the final state of the structure, enabling faster analysis for inverse design. This work presents a lumped-element model to determine the final shape of our metastructure in terms of the number of units, spatial distribution, and unit cell geometric parameters. We explore the effect of interrelations between units and their spatial arrangement in our metastructure's global stable shape, enabling us to target specific target positions. We further examine the interaction between units and their role in generating geometric frustration within the structure and allowing us to determine optimal strategies to leverage all these multiple states in applications such as soft robotics and mechanical computation. This opens a route for the fast design of multistable soft robots and shapes targeting of soft metastructures.