Selective buckling via states of self-stress in topological metamaterials
arXiv:1502.03396 · doi:10.1073/pnas.1502939112
Abstract
States of self-stress, tensions and compressions of structural elements that result in zero net forces, play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable mechanical properties. We exploit a class of recently introduced states of self-stress analogous to topological quantum states to sculpt localized buckling regions in the interior of periodic cellular metamaterials. Although the topological states of self stress arise in the linear response of an idealized mechanical frame of harmonic springs connected by freely-hinged joints, they leave a distinct signature in the nonlinear buckling behaviour of a cellular material built out of elastic beams with rigid joints. The salient feature of these localized buckling regions is that they are indistinguishable from their surroundings as far as material parameters or connectivity of their constituent elements are concerned. Furthermore, they are robust against a wide range of structural perturbations. We demonstrate the effectiveness of this topological design through analytical and numerical calculations as well as buckling experiments performed on two- and three-dimensional metamaterials built out of stacked kagome lattices.
Published version: edits to text, notation; added supplementary figure and discussion. 14 pages, 9 figures, see http://www.lorentz.leidenuniv.nl/~paulose/topological-buckling/ for accompanying videos
References in corpus (5)
Cited by in corpus (91)
- Topological mechanics of gyroscopic metamaterials
- Topologically protected elastic waves in phononic metamaterials
- Combinatorial Design of Textured Mechanical Metamaterials
- Static non-reciprocity in mechanical metamaterials
- Classification of topological phonons in linear mechanical metamaterials
- Observation of topological valley modes in an elastic hexagonal lattice
- Artificial gauge fields in materials and engineered systems
- Topological mechanics of origami and kirigami
- Transformable topological mechanical metamaterials
- Topological Phase Transition in Mechanical Honeycomb Lattice
- Non-Hermitian band topology and skin modes in active elastic media
- Mechanical Weyl Modes in Topological Maxwell Lattices
- Topological phonons and Weyl lines in 3 dimensions
- Automatic Design of Mechanical Metamaterial Actuators
- Sonic Landau-level lasing and synthetic gauge fields in mechanical metamaterials
- Topological Thermal Hall Effect in Frustrated Kagomé Antiferromagnets
- Amplitude-dependent topological edge states in nonlinear phononic lattices
- Topological defects produce exotic mechanics in complex metamaterials
- Tunable failure: control of rupture through rigidity
- Geared topological metamaterials with tunable mechanical stability
- Soft self-assembly of Weyl materials for light and sound
- Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies
- Dynamical Majorana Edge Modes in a Broad Class of Topological Mechanical Systems
- Topological edge floppy modes in disordered fiber networks
- Fracturing of topological Maxwell lattices
- Nonlinear non-Hermitian higher-order topological laser
- Topological Edge Modes by Smart Patterning
- Mechanics of disordered auxetic metamaterials
- Line nodes, Dirac points and Lifshitz transition in 2D nonsymmorphic photonic crystals
- Switchable phonon diodes using nonlinear topological Maxwell lattices
- Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system
- Anharmonic interatomic force constants and thermal conductivity from Grüneisen parameters: an application to graphene
- Geometry of wave propagation on active deformable surfaces
- Topology in non-linear mechanical systems
- Universal Continuum Theory for Topological Edge Soft Modes
- Directional mechanical response in the bulk of topological metamaterials
- Buckling of thermalized elastic sheets
- Topological mechanics in quasicrystals
- Localizing softness and stress along loops in three-dimensional topological metamaterials
- Rigidity percolation control of the brittle-ductile transition in disordered networks
- Topologically protected interface phonons in two-dimensional nanomaterials: hexagonal boron nitride and silicon carbide
- Kink-antikink asymmetry and impurity interactions in topological mechanical chains
- Simple views on symmetries and dualities in the theory of elasticity
- Topological boundary modes in jammed matter
- Density scaling in the mechanics of a disordered mechanical meta-material
- Mechanical Graphene
- Topological dynamics of gyroscopic and Floquet lattices from Newton's laws
- Topological elasticity of flexible structures
- Thermal engineering in low-dimensional quantum devices: a tutorial review of nonequilibrium Green's function methods
- Soft mechanical metamaterials with transformable topology protected by stress caching
- Signatures of Topological Phonons in Superisostatic Lattices
- Elasticity of Jammed Packings of Sticky Disks
- Switchable topological phonon channels
- A classification of magnetic frustration and metamaterials from topology
- Bi-stability resistant to fluctuations
- Response evolution of mechanical metamaterials under architectural transformations
- Origin and localization of topological band gaps in gyroscopic metamaterials
- Free energy of singular sticky-sphere clusters
- Self-Ordering of Buckling, Bending, Bumping Beams
- Reversible signal transmission in an active mechanical metamaterial
- Topology and geometry of spin origami
- Supersymmetry "protected" topological phases of isostatic lattices and kagome antiferromagnets
- Omnimodal topological polarization of bilayer networks: analysis in the Maxwell limit and experiments on a 3D-printed prototype
- Experimental demonstration of position-controllable topological interface states in high-frequency topological integrated circuits
- Quench dynamics and bulk-edge correspondence in nonlinear mechanical systems
- Fractional solitons in non-Euclidian elastic plates
- Wang tiles enable combinatorial design and robot-assisted manufacturing of modular mechanical metamaterials
- Controlling the Deformation of Metamaterials: Corner Modes via Topology
- Fully-Polarized Topological Isostatic Metamaterials in Three Dimensions
- Solitons in one-dimensional mechanical linkage
- Robustness of stress focusing in soft lattices under topology-switching deformation
- Transition fronts and their universality classes
- Soft topological modes protected by symmetry in rigid mechanical metamaterials
- Nonlinear topological phase diagram in dimerized sine-Gordon model
- Topological mechanical metamaterial with nonrectilinear constraints
- Topological interface states mediated by spontaneous symmetry breaking
- Capillary-driven binding of thin triangular prisms at fluid interfaces
- Scattering theory from artificial piezoelectric-like meta-atoms and molecules
- Classical topological paramagnetism
- Scalable 3D printing for topological mechanical metamaterials
- Non-reciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems
- Architecting mechanisms of damage in topological metamaterials
- Corner-Sharing Tetrahedra for Modeling Micro-Structure
- Omnidirectional domain wall modes protected by fragile topological states
- A study of deformation localization in nonlinear elastic lattices
- Cell augmentation framework for topological lattices
- 3D Topologically Polarized Elastic Metamaterials Enable Asymmetric Energy Isolation at Low Frequencies
- Nonlinear dynamical topological phases in Cooper-pair box array
- Three-dimensional Kinematic Metamaterial with tuneable directional permeability
- 4D printing of mechanical metamaterials
- Three-dimensional transformable modular kirigami based programmable architected materials