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.

连续弹性板具有无限的自由度：根据所施加的载荷，其形状取决于总能量的最小值，取决于所用的材料。控制变形结构的形状的可能性在多个领域受到越来越多的关注。在这方面，如果考虑一种经典的弹性板，通常不可能调节该材料的弹性特性以在该板可能具有的无限变形模式之间选择所需的一种。我们提出了一个原型案例，试图满足这个愿望，为微结构的几何结构的系统设计开辟了道路，以完全独立于所施加的载荷来完全控制系统的形状。对于仅具有一个自由度的薄板，提出了一种新颖而简单的结构。该板实现为由沿侧面相互铰接的刚性相等的六边形瓷砖组成的棋盘形装饰，并且无论施加何种载荷，它都可以仅一种方式变形，即变形为预定的同质弹性表面。这种棋盘形板在弯曲时也具有显着的拉力性能，单轴弯曲中的横向曲率和纵向曲率之比达到大于1的值。在离散和连续水平上的建模假设和分析结果均通过对添加制造的双材料样本进行的测试得到验证，表明可以通过控制六边形的几何形状来设计变形构造。所提出的用于仅以一个自由度实现辅助板的架构具有高度的可扩展性，并且易于制造，并且可以在辅助棚架，假体应力防护罩，能量收集器和可穿戴设备中找到应用。