Topological elasticity of flexible structures

Abstract

Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via micromorphic continuum elasticity, which allows highly nonuniform deformations (missed in conventional elasticity) within unit cells that nevertheless vary smoothly between cells. We show that the bulk microstructure gives rise to boundary elastic terms. Discrete lattice theories have shown that critically coordinated structures possess a topological invariant which determines the placement of low-energy modes on edges of such a system. We show that in continuum systems a new topological invariant emerges which relates the difference in the number of such modes between two opposing edges. Guided by the continuum limit of the lattice structures, we identify macroscopic experimental observables for these topological properties that may be observed independently on a new length scale above that of the microstructure.

arXiv comment13 pages, 9 attachments for a total of 6 figures

References in corpus (26)

• Topological Boundary Modes in Isostatic Lattices
• Modeling semiflexible polymer networks
• On the feasibility of pentamode mechanical metamaterials
• Static non-reciprocity in mechanical metamaterials
• Topological modes bound to dislocations in mechanical metamaterials
• Amorphous topological insulators constructed from random point sets
• Nonlinear conduction via solitons in a topological mechanical insulator
• Experimental realization of on-chip topological nanoelectromechanical metamaterials
• Selective buckling via states of self-stress in topological metamaterials
• Designing allostery-inspired response in mechanical networks
• Topological mechanics of origami and kirigami
• Transformable topological mechanical metamaterials
• Observation of topologically protected helical edge modes in Kagome elastic plates
• Mechanical Weyl Modes in Topological Maxwell Lattices
• A characteristic lengthscale causes anomalous size effects and boundary programmability in mechanical metamaterials
• Topological phases without crystalline counterparts
• Architecture and Co-Evolution of Allosteric Materials
• Topological Sound and Flocking on Curved Surfaces
• Intrinsically polar elastic metamaterials
• Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies
• Fracturing of topological Maxwell lattices
• Mechanics of disordered auxetic metamaterials
• Directional mechanical response in the bulk of topological metamaterials
• Topological mechanics in quasicrystals
• Conformational Control of Mechanical Networks
• Topological elasticity of non-orientable ribbons

Cited by in corpus (10)

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• Simple views on symmetries and dualities in the theory of elasticity
• Modelling planar kirigami metamaterials as generalized elastic continua
• Learning to self-fold at a bifurcation
• Odd elasticity and topological waves in active surfaces
• Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity
• Geometric control of topological dynamics in a singing saw
• Classifying topological floppy modes in the continuum
• Topological Floppy Modes in Epithelial Tissues