Auxetic materials have a negative Poisson’s ratio and are of significant interest in applications that include impact mitigation, membrane separations and biomedical engineering. While there are numerous examples of structured materials that exhibit auxetic behavior, the examples of engineered auxetic structures is largely limited to periodic lattice structures that are limited to directional or anisotropic auxetic response. Structures that exhibit a three-dimensionally isotropic auxetic response have been, unfortunately, slow to evolve. Here we introduce an inverse design algorithm based on global node optimization to design three-dimensional auxetic metamaterial structures from disordered networks. After specifying the target Poisson’s ratio for a structure, an inverse design algorithm is used to adjust the positions of all nodes in a disordered network structure until the desired mechanical response is achieved. The proposed algorithm allows independent control of shear and bulk moduli, while preserving the density and connectivity of the networks. When the angle bending stiffness in the network is kept low, it is possible to realize optimized structures with a Poisson’s ratios as low as −0.6. During the optimization, the bulk modulus of these networks decreases by almost two orders of magnitude, but the shear modulus remains largely unaltered. The materials designed in this manner are fabricated by dual-material 3D-printing, and are found to exhibit the mechanical responses that were originally encoded in the computational design engine. The approach proposed here provides a materials-by-design platform that could be extended for engineering of optical, acoustic, and electrical properties, beyond the design of auxetic metamaterials.

拉胀材料具有负泊松比，在减轻冲击、膜分离和生物医学工程等应用中具有重要意义。虽然存在许多表现出拉胀行为的结构化材料的示例，但是工程拉胀结构的示例很大程度上限于仅限于定向或各向异性拉胀响应的周期性晶格结构。不幸的是，表现出三维各向同性拉胀响应的结构发展缓慢。在这里，我们介绍一种基于全局节点优化的逆向设计算法，用于从无序网络设计三维拉胀超材料结构。在指定结构的目标泊松比后，使用逆向设计算法来调整无序网络结构中所有节点的位置，直到达到所需的机械响应。所提出的算法允许独立控制剪切模量和体积模量，同时保留网络的密度和连接性。当网络中的角弯曲刚度保持较低时，可以实现泊松比低至-0.6的优化结构。在优化过程中，这些网络的体积模量降低了近两个数量级，但剪切模量基本保持不变。以这种方式设计的材料是通过双材料 3D 打印制造的，并且被发现表现出最初在计算设计引擎中编码的机械响应。这里提出的方法提供了一个材料设计平台，可以扩展到光学、声学和电学特性的工程，超越拉胀超材料的设计。