Cell augmentation framework for topological lattices
arXiv:2301.10376 · doi:10.1103/PhysRevB.108.L020301
Abstract
Maxwell lattices are characterized by an equal number of degrees of freedom and constraints. A subset of them, dubbed topological lattices, are capable of localizing stress and deformation on opposing edges, displaying a polarized mechanical response protected by the reciprocal-space topology of their band structure. In two dimensions, the opportunities for topological polarization have been largely restricted to the kagome and square lattice benchmark configurations, due to the non-triviality of generating arbitrary geometries that abide by Maxwell conditions. In this work, we introduce a generalized family of augmented topological lattices that display full in-plane topological polarization. We explore the robustness of such polarization upon selection of different augmentation criteria, with special emphasis on augmented configurations that display dichotomous behavior with respect to their primitive counterparts. We corroborate our results via intuitive table-top experiments conducted on a lattice prototype assembled from 3D-printed mechanical links.
References in corpus (21)
- Topological Insulators
- Topological insulators and superconductors
- Topological Boundary Modes in Isostatic Lattices
- Bistable Auxetic Mechanical Metamaterials Inspired by Ancient Geometric Motifs
- Topological modes bound to dislocations in mechanical metamaterials
- Nonlinear conduction via solitons in a topological mechanical insulator
- Selective buckling via states of self-stress in topological metamaterials
- Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
- Transformable topological mechanical metamaterials
- Mechanical Weyl Modes in Topological Maxwell Lattices
- Topological phonons and Weyl lines in 3 dimensions
- Intrinsically polar elastic metamaterials
- Dualities and non-Abelian mechanics
- Topological defects produce exotic mechanics in complex metamaterials
- Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies
- Effective Medium Theory of Filamentous Triangular Lattice
- Localizing softness and stress along loops in three-dimensional topological metamaterials
- Signatures of Topological Phonons in Superisostatic Lattices
- Symmetry of the phonon landscape across the duality boundary of twisted kagomes lattices
- 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