Design of binary stiffness adaptive elements with tunable linear and nonlinear response

Realizing reprogrammable structures with adaptation in response to unknown environmental stimuli remains challenging, as existing structures are limited to adaptations defined during design and manufacturing. Mechanical metamaterials composed of individually adaptive unit cells with tunable stiffness response can offer robust adaptation to unknown environments. However, existing variable-stiffness technologies provide limited control over stiffness response. Here, we present binary stiffness adaptive elements that reversibly switch between discrete axial stiffness states by reconfiguring the internal load path between compliant spring-like arches and a stiff column using an electromagnetic actuator. The magnitude and linearity of the adaptive stiffness response can be tuned through geometric parameters. We design elements exhibiting both linear and nonlinear force-displacement responses, characterize their mechanical response, and develop finite element models to capture the stiffness adaptation supported by experimental validation or calibrated by experiments. We also present an inverse design framework based on an evolutionary optimization algorithm to target specific stiffness curves. Integrated into a lattice metamaterial, these tunable binary stiffness elements provide a practical mechanism for reprogrammable adaptive structures through the linear or nonlinear mechanical response of each element.