One-Degree-of-Freedom Mechanical Metamaterials with Arbitrary Prescribability and Rapid Reprogrammability of Force-Displacement Curves.

Mechanical metamaterials, by introducing porous structures into the materials, can achieve complex nonlinear responses through the large deformation of structures, which support a new generation of impact energy absorption and vibration damping systems, wearable electronics, and tactile simulation devices. However, arbitrarily customizable stress-strain curves have yet to be achieved by existing mechanical metamaterials, which are inherently multi-degree-of-freedom (multi-DOF) deformable systems, and their deformation sequence is influenced by the minimum energy gradient principle. Multi-DOF metamaterials behave like underactuated systems, where the number of degrees of freedom exceeds the number of actuators. As a result, their deformation is controlled by the material's elastic forces, inertial forces, and boundary constraints. Here, we propose a novel composition of elastic components integrated with one-degree-of-freedom (1-DOF) kinematic bases, forming a fully actuated system in which the number of actuators equals the number of degrees of freedom. The deformation of each elastic component is governed by its designed 1-DOF kinematic path. Consequently, the stress-strain profile can be arbitrarily prescribed, for instance, controlled multistage strain softening curve is achievable, as the principle of minimum energy gradient does not affect the deformation sequence dictated by the 1-DOF kinematic base. Furthermore, a class of shape memory alloys (SMAs) is introduced as active components to enable rapid in situ property change, providing versatility in switching between different target responses. The analytical inverse design method, numerical analysis, parametric study of different target responses, and experimental validation are carried out. Lastly, preliminary demonstrations of designable anisotropic nonlinear responses are presented.