Topological defects produce exotic mechanics in complex metamaterials

The basic tenet of metamaterials is that the architecture controls the physics1,2,3,4,5,6,7,8,9,10,11,12. So far, most studies have considered defect-free architectures. However, defects, and particularly topological defects, play a crucial role in natural materials13,14,15. 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.