Recent advancements in reprogrammable metamaterials have enabled the development of intelligent matters with variable special properties in situ. These metamaterials employ intra-element physical reconfiguration and inter-element structural transformation. However, existing mono-characteristic homo-element mechanical metamaterials have limited reprogramming functions. Here, we introduce a reprogrammable mechanical metamaterial composed of origami elements with heterogeneous mechanical properties, which achieves various mechanical behavior patterns by functional group transformations and ring reconfigurations. Through the anisotropic assembly of two heterogeneous elements into a functional group, we enable mechanical behavior switching between positive and negative stiffness. The resulting polygonal ring exhibits rotational deformation, zero Poisson’s ratio stretching/compression deformation, and negative Poisson’s ratio auxetic deformation. Arranging these rings periodically yields homogeneous metamaterials. The reconfiguration of quadrilateral rings allows for continuous fine-tunability of the mechanical response and negative Poisson’s ratio. This mechanical metamaterial could provide a versatile material platform for reprogrammable mechanical computing, multi-purpose robots, transformable vehicles and architectures at different scales.

Analysis of cantilever-based piezoelectric energy harvesting systems is usually performed using coupled equations that represent the mechanical displacement and the voltage output. These equations are then solved simultaneously. In contrast to this representation, we use analytical solutions of the governing equation to derive an algebraic equation of the power as a function of the beam displacement, electromechanical coefficients, and the load resistance. Such an equation can be more useful in the design of such harvesters. Particularly, the mechanical displacement is computed from a mechanical governing equation with modified natural frequency and damping ratio that account for the electromechanical coupling. The voltage and the harvested power are then obtained by relating them directly to the mechanical displacement. We validate the proposed analysis by comparing its solution including the tip displacement and harvested power with those of numerical simulations of the governing equations. To demonstrate the generality of the proposed approach, we consider the cases of base excitation, galloping, and autoparametric vibration. The model proposed in this study simplifies the electromechanical coupling problem for practical applications of cantilever-beam piezoelectric energy harvesting systems.