Reversible negative compressibility metamaterials inspired by Braess’s Paradox

Negative compressibility metamaterials have attracted significant attention due to their distinctive properties and promising applications. Negative compressibility has been interpreted in two ways. Regarding the negative compressibility induced by a uniaxial load, it can only occur abruptly when the load reaches a certain threshold. Hence, it can be termed as transient negative compressibility. However, fabrication and experiments of such metamaterials have rarely been reported. Herein, we demonstrate them. Inspired by Braess’s paradox, a novel mechanical model is proposed with reversible negative compressibility. It shows multiple types of force responses during a loading-unloading cycle, including transient negative compressibility and hysteresis. Phase diagrams are employed to visualize the relationship between force responses and system parameters. Besides, explicit expressions for the conditions and intensity of negative compressibility are obtained for design and optimization. The model replacement method inspired by compliant mechanism design is then introduced to derive specific unit cell structures, thus avoiding intuition-based approaches. Additive manufacturing technology is utilized to fabricate the prototypes, and negative compressibility is validated via simulations and experiments. Furthermore, it is demonstrated that metamaterials with transient negative compressibility can be activated through electrical heating and can function as actuators, thereby possessing machine-like properties. The proposed mechanical metamaterial and the introduced design methodology have potentials to impact micro-electromechanical systems, force sensors, protective devices, and other applications.