Topology in non-linear mechanical systems

Abstract

Many advancements have been made in the field of topological mechanics. The majority of the works, however, concerns the topological invariant in a linear theory. We, in this work, present a generic prescription of defining topological indices which accommodates non-linear effects in mechanical systems without taking any approximation. Invoking the tools of differential geometry, a Z-valued quantity in terms of the Poincare-Hopf index, that features the topological invariant of non-linear zero modes (ZMs), is predicted. We further identify one type of topologically protected solitons that are robust to disorders. Our prescription constitutes a new direction of searching for novel topologically protected non-linear ZMs in the future.

References in corpus (26)

• Topological Insulators
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators with Inversion Symmetry
• Topological Acoustics
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• Topological Boundary Modes in Isostatic Lattices
• Topological mechanics of gyroscopic metamaterials
• Topological modes bound to dislocations in mechanical metamaterials
• Nonlinear conduction via solitons in a topological mechanical insulator
• On the $Z_2$ classification of Quantum Spin Hall Models
• Selective buckling via states of self-stress in topological metamaterials
• Topological mechanics of origami and kirigami
• Mechanical Weyl Modes in Topological Maxwell Lattices
• Coriolis Force Induced Quantum Hall Effect for Phonons
• Topological phonons and Weyl lines in 3 dimensions
• Topological edge floppy modes in disordered fiber networks
• Fracturing of topological Maxwell lattices
• Phonon analogue of topological nodal semimetals
• Topological mechanics in quasicrystals
• Kink-antikink asymmetry and impurity interactions in topological mechanical chains
• A classification of magnetic frustration and metamaterials from topology
• Topology and geometry of spin origami
• Controlling the Deformation of Metamaterials: Corner Modes via Topology
• Solitons in one-dimensional mechanical linkage
• Emergent gauge dynamics of highly frustrated magnets

Cited by in corpus (9)

• Topological Invariant and Anomalous Edge Modes of Strongly Nonlinear Systems
• Synthetically Non-Hermitian Nonlinear Wave-like Behavior in a Topological Mechanical Metamaterial
• Chiral edge soliton in nonlinear Chern systems
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Controlling the configuration space topology of mechanisms
• Nonlinear topological phase diagram in dimerized sine-Gordon model
• Nonlinear dynamics of topological helicity wave in a frustrated skyrmion string
• Nonlinear topological Toda quasicrystal
• Nonlinear dynamical topological phases in Cooper-pair box array