The basic tenet of metamaterials is that the architecture controls the physics^{1,2,3,4,5,6,7,8,9,10,11,12}. So far, most studies have considered defect-free architectures. However, defects, and particularly topological defects, play a crucial role in natural materials^13,14,15. Here we provide a systematic strategy for introducing such defects in mechanical metamaterials. We first present metamaterials that are a mechanical analogue of spin systems with tunable ferromagnetic and antiferromagnetic interactions, then design an exponential number of frustration-free metamaterials and finally introduce topological defects by rotating a string of building blocks in these metamaterials. We uncover the distinct mechanical signature of topological defects using experiments and simulations, and leverage this to design complex metamaterials in which external forces steer deformations and stresses towards complementary parts of the system. Our work presents a new avenue to systematically including spatial complexity, frustration and topology in mechanical metamaterials.

超材料的基本原则是架构控制物理^{1,2,3,4,5,6,7,8,9,10,11,12}。到目前为止，大多数研究都考虑了无缺陷架构。然而，缺陷，尤其是拓扑缺陷，在天然材料中起着至关重要的作用^13,14,15. 在这里，我们提供了一种在机械超材料中引入此类缺陷的系统策略。我们首先提出了具有可调谐铁磁和反铁磁相互作用的自旋系统的机械模拟超材料，然后设计了指数数量的无挫折超材料，最后通过旋转这些超材料中的一串构建块来引入拓扑缺陷。我们通过实验和模拟揭示了拓扑缺陷的独特机械特征，并利用它来设计复杂的超材料，其中外力将变形和应力引导至系统的互补部分。我们的工作为系统地包括机械超材料中的空间复杂性、挫折和拓扑结构提供了一条新途径。