Intrinsically Polar Elastic Metamaterials

Abstract

The ability to design and fabricate materials with tailored mechanical properties, combined with immunity to damage, is a frontier of materials engineering. For example, materials which are characterized by elastic properties that depend on the position inside a medium are required in applications where structural stability has to be combined with a soft and compliant surface, like in impact protection and cushioning. A gradient in the elastic properties can be built from a single material, varying gradually the bulk porosity of the material or its geometrical structure. However, if such a gradient is built into the material at production, damage or wearing over time might expose unwanted elastic properties. Here, we implement a design principle for a spatially inhomogeneous material based on topological band-theory for mechanical systems. The resulting inhomogeneity is stable against wearing and even cutting the material in half. We show how, by creating a periodic elastic material with topological properties, one can create an intrinsically polar behavior, where a face with a given surface normal is stiff while its opposing face is soft.a The characteristic properties of periodic materials are captured in their phononic spectrum, i.e., their dispersion relation, which contains information ranging from the material's quasi-static elastic response (at very low frequencies) to its thermal conductivity (at higher frequencies). In topological (polar) materials, the phonon spectrum, and with it the linked material properties, are different on two opposing surfaces of the material. Uniquely to topological materials, the polar behavior is stable and remains preserved when these materials are cut or fractured, as shown in Fig. 1a, b: No matter how much of our material is lost to a fracture, or wearing during use, the asymmetry in the mechanical response remains the same [8][9][10][11]. Note, that these topological features are linked to surface modes whose penetration depth introduces a new length-scale and hence the stability with respect to wearing and fracturing is not bound to the microscopic unit cell size. This similarity to the polarity of a dielectric motivates the term of an intrinsically polar elastic metamaterial.As it turns out, the simplest lattice that lends itself to the design of such a polar metamaterial has another topologically protected feature in its phononic spectrum: Lines of zero-frequency excitation that span throughout the whole Brillouin zone and which cannot be gapped out [12]. Such nodal, or Weyl lines [10,[12][13][14][15] are of considerable recent interest in electronic systems [15] as they mediate non-local magneto-transport. In our mechanical setup, we find clear experimental evidence of these Weyl lines and we further capitalize on their presence to fine tune the elastic response.We design our polar elastic materials as a truss-like, pea This is the pre-peer reviewed version of the following article: Adv. Mater. 1700540 (2017), which has been published in final form at URL. This articl...

Soft self-assembly of Weyl materials for light and sound

“…Note that the Weyl points we consider here generically occur at finite frequency, and do not require a particular symmetry. In contrast, mechanical symmetry-protected Weyl points (similar to Dirac points in graphene) and Weyl lines occur at zero frequency [11][12][13][14][15]. There, a chiral symmetry is essential to define the topological quantities, and in turn reveals a duality between zero-frequency free mechanical motions and so-called self-stress modes [16][17][18][19][20][21].…”

Localizing softness and stress along loops in 3D topological metamaterials

“…Large-scale and localized deformations are deeply intertwined, as can be seen in demonstrations in which topological soft modes are created or destroyed by applying large uniform strains (34). For many applications, such as cushioning (35), programmed assembly (36), or controlled failure (37), materials need to be designed with nonuniform yield behavior. Deformation or failure at a specified region can be programmed via a combination of topological polarization and localized defects (37,38).…”

“…Deformation or failure at a specified region can be programmed via a combination of topological polarization and localized defects (37,38). Soft regions can selectively achieve large displacements [for example, in self-folding origami (36,39,40)] and isolate the rest of the material from strain (35).…”

“…Although there are a number of examples of isostatic periodic structures in one, two, and three dimensions, the 3D case is unique, because all prior realizations of 3D isostatic lattices include large-scale periodic deformations along continuous lines in momentum space (15,35,37). These Weyl lines define families of periodic soft modes in the material bulk and contain a number of modes that scales with the linear size of the structure.…”

“…As ref. 35 explores, Weyl lines can be useful to create a metamaterial surface with anisotropic elasticity, but to create a material with a top surface that is much softer than the bottom, it proves necessary to collapse two Weyl lines on top of each other. An alternative would be to find a metamaterial without Weyl lines.…”