Design and Visualization of a Hierarchical Metamaterial with Tunable Stiffness.

Metamaterials with stiffness tunability have demonstrated great potential in mechanical systems that operate in variable environments. However, most existing stiffness-tunable metamaterials exhibit high-dimensional and nonlinear structure-property relationships, which hinder precise on-demand tuning and real-time stiffness visualization. Here, we present a reconfigurable hierarchical metamaterial that integrates stiffness tunability, linear structure-property relationship, and real-time self-sensing stiffness visualization into a unified platform. Kinematic analysis shows that the hierarchical metamaterial can be reconfigured through kinematic bifurcations into various single- and multi-level configurations with different numbers of active hinges, and maintain a single degree of freedom in each deformation path. Subsequently, a linear relationship between the number of active hinges and the stiffness of the metamaterial is established through theoretical modelling and verified by experiments, allowing a wide range of tunable stiffness. Furthermore, mechanical logic circuits are embedded into the metamaterial to map transitions between units at different levels to electrical outputs, achieving real-time stiffness visualization via light-emitting diode (LED) states without external sensors. This proposed metamaterial, and more generally, the structure-property-information integration design framework, will greatly advance the development of intelligent adaptive systems.