Quantifying efficient shape-shifting: Energy barrier measurement in multi-stable lattice metamaterials

Shape-shifting between multiple stable deformation states offers attractive pathways to design adaptive structures. Ideas have been conceptualised in diverse fields, including soft robotics and aerospace engineering. The success of shape-shifting relies on overcoming the energy barrier separating adjacent stable configurations, which necessitates efficient actuation strategies. Recently, multistable mechanical metamaterials have been designed with shape-shifting controlled by an actuator at the local scale, i.e with embedded actuation. This local, embedded actuation creates challenges for quantifying the energy barriers required for shape-shifting. Specifically, the local actuation requires a pair of forces with opposite directions and the direction of the forces must remain constant throughout the entire loading process. Moreover, the loading points must move freely in a direction perpendicular to the loading direction. We present a novel bi-axial test rig for a typical multi-stable lattice metamaterial that accurately determines the energy barrier between stable states by using an embedded actuator and inducing shape-shifting. Our experimental design features two independent actuation systems operating at different length scales: a primary one for a globally applied axial compression of the metamaterial, and a secondary local system for triggering shape-shifting between different stable configurations. Experimental data obtained using this bespoke test rig unveil the metamaterial's response to local, embedded actuation. Excellent agreement with finite element simulations is observed, demonstrating the effectiveness of the test setup in providing measurements of the energy barrier. This work provides a valuable benchmark for measuring energy barriers in multi-stable metamaterials and paves the way for rigorous validation and verification of novel functional metamaterial and structures that leverage shape-shifting mechanisms.