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Mechanical metamaterials present a promising platform for seemingly impossible mechanics. They often require incompatibility of their elementary building blocks, yet a comprehensive understanding of its role remains elusive. Relying on an analogy to ferromagnetic and antiferromagnetic binary spin interactions, we present a universal approach to identify and analyze topological mechanical defects for arbitrary building blocks. We underline differences between two- and three-dimensional metamaterials, and show how topological defects can steer stresses and strains in a controlled and non-trivial manner and can inspire the design of materials with hitherto unknown complex mechanical response.
Topological mechanics can realize soft modes in mechanical metamaterials in which the number of degrees of freedom for particle motion is finely balanced by the constraints provided by interparticle interactions. However, solid objects are generally
Hyperbolic metamaterials (HMMs) are highly anisotropic optical materials that behave as metals or as dielectrics depending on the direction of propagation of light. They are becoming essential for a plethora of applications, ranging from aerospace to
Mechanical metamaterials are architected manmade materials that allow for unique behaviors not observed in nature, making them promising candidates for a wide range of applications. Existing metamaterials lack tunability as their properties can only
In the dense metal-organic framework Na[Mn(HCOO)$_3$], Mn$^{2+}$ ions ($S=frac{5}{2}$) occupy the nodes of a `trillium hyperkagome net. We show that this material exhibits a variety of behaviour characteristic of geometric frustration: the Neel trans
Active matter is ubiquitous in biology and becomes increasingly more important in materials science. While numerous active systems have been investigated in detail both experimentally and theoretically, general design principles for functional active