Design of auxetic plates with only one degree of freedom

A continuum elastic plate has infinite degrees of freedom: according to the applied loads, it assumes the shape that the minimization of the total energy prescribes, in dependence of the material it is made of. The possibility to control the shape of a morphing structure is receiving an increasing attention in several fields; in this connection, if a classical elastic plate is considered, it is not possible, in general, to tune the elastic properties of the material in order to select, between the infinite deformation modes the plate may have, the one desired. We present a prototypical case that tries to satisfy this desideratum, opening the way to the systematic design of microstructure's geometries to fully control a system's shape independently of the applied loads. A novel yet simple architecture for thin plates having only one degree of freedom is proposed. The plate is realized as a tessellation composed by rigid equal hexagonal tiles hinged to each other along the sides, and it can deform in just one way, that is, into a predetermined synclastic surface, whatever loads are applied to it. Such tessellated plate also has a remarkable auxetic behavior in bending, with the ratio between transverse and longitudinal curvatures in uniaxial bending reaching values larger than one. Modeling assumptions and analysis results, at both the discrete and the continuum level, are verified by tests carried out onto additively manufactured bi-material specimens, showing that it is possible to design the deformed configuration by controlling the hexagons’ geometry. The proposed architecture for realizing auxetic plates with only one degree of freedom is highly scalable and easily manufacturable, and it can find applications for auxetic scaffolds, prosthetic stress shields, energy harvesters, and wearable devices.