After a decade of periodic truss-, plate-, and shell-based architectures having dominated the design of metamaterials, we introduce the non-periodic class of spinodoid topologies. Inspired by natural self-assembly processes, spinodoid metamaterials are a close approximation of microstructures observed during spinodal phase separation. Their theoretical parametrization is so intriguingly simple that one can bypass costly phase-field simulations and obtain a rich and seamlessly tunable property space. Counter-intuitively, breaking with the periodicity of classical metamaterials is the enabling factor to the large property space and the ability to introduce seamless functional grading. We introduce an efficient and robust machine learning technique for the inverse design of (meta-)materials which, when applied to spinodoid topologies, enables us to generate uniform and functionally graded cellular mechanical metamaterials with tailored direction-dependent (anisotropic) stiffness and density. We specifically present biomimetic artificial bone architectures that not only reproduce the properties of trabecular bone accurately but also even geometrically resemble natural bone.

在超常材料的设计占据主导地位的十年周期的基于桁架，板和壳的体系结构之后，我们介绍了非周期性的旋节线形拓扑。受自然自组装过程启发，旋节线超材料是在旋节线相分离过程中观察到的微观结构的近似值。它们的理论参数设置非常简单，可以绕过昂贵的相场模拟并获得丰富且无缝可调的属性空间。与直觉相反，打破经典超材料的周期性是导致大型属性空间以及引入无缝功能分级的能力的促成因素。我们针对（元）材料的逆向设计引入了一种高效且鲁棒的机器学习技术，该技术在应用于Spinodoid拓扑时，使我们能够生成具有定制的方向相关（各向异性）的刚度和密度的均匀且功能渐变的蜂窝机械超材料。我们专门介绍了仿生人造骨结构，该结构不仅可以准确地再现小梁骨的特性，而且在几何上还类似于天然骨。