Localizing softness and stress along loops in three-dimensional topological metamaterials

Abstract

Topological states can be used to control the mechanical properties of a material along an edge or around a localized defect. The surface rigidity of elastic networks is characterized by a bulk topological invariant called the polarization; materials with a well-defined uniform polarization display a dramatic range of edge softnesses depending on the orientation of the polarization relative to the terminating surface. However, in all three-dimensional mechanical metamaterials proposed to date, the topological edge modes are mixed with bulk soft modes and so-called Weyl loops. Here, we report the design of a gapped 3D topological metamaterial with a uniform polarization that displays a corresponding asymmetry between the number of soft modes on opposing surfaces and, in addition, no bulk soft modes. We then use this construction to localize topological soft modes in interior regions of the material by including defect structures---dislocation loops---that are unique to three dimensions. We derive a general formula that relates the difference in the number of soft modes and states of self-stress localized along the dislocation loop to the handedness of the vector triad formed by the lattice polarization, Burgers vector, and dislocation-line direction. Our findings suggest a novel strategy for pre-programming failure and softness localized along lines in 3D, while avoiding extended periodic failure modes associated with Weyl loops.

23 pages, 4 figures

References in corpus (8)

• Topological Photonics
• Topological Acoustics
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Observation of a phononic quadrupole topological insulator
• Programmable Mechanical Metamaterials
• Topological modes bound to dislocations in mechanical metamaterials
• Nonlinear conduction via solitons in a topological mechanical insulator
• Intrinsically polar elastic metamaterials

Cited by in corpus (14)

• Soft self-assembly of Weyl materials for light and sound
• Proteins: the physics of amorphous evolving matter
• Soft mechanical metamaterials with transformable topology protected by stress caching
• Signatures of Topological Phonons in Superisostatic Lattices
• Reversible signal transmission in an active mechanical metamaterial
• Topological Flexural Modes in Polarized Bilayer Lattices
• Omnimodal topological polarization of bilayer networks: analysis in the Maxwell limit and experiments on a 3D-printed prototype
• Fully-Polarized Topological Isostatic Metamaterials in Three Dimensions
• Controlling the Deformation of Metamaterials: Corner Modes via Topology
• Robustness of stress focusing in soft lattices under topology-switching deformation
• Soft topological modes protected by symmetry in rigid mechanical metamaterials
• Scalable 3D printing for topological mechanical metamaterials
• Cell augmentation framework for topological lattices
• Realizations of Isostatic Material Frameworks