Topology in Nonlinear Mechanical Systems

2021/04/26 by Po-Wei Lo, Krishanu Roychowdhury, Bryan Chen +5
Engineering · Mathematics · Physics and Astronomy · #Combinatorics #Dynamics and Control of Mechanical Systems #Mathematics #Nonlinear system #Physics #Quantum mechanics #Topology (electrical circuits) #cond-mat.soft

paper · pdf · doi:10.1103/physrevlett.127.076802

published as Phys. Rev. Lett. 127, 076802 (2021)

arxiv created 2021/04/26 · openalex publication_date 2021/08/13 · arxiv updated 2021/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Many advancements have been made in the field of topological mechanics. The majority of the work, however, concerns the topological invariant in a linear theory. In this Letter, we present a generic prescription to define topological indices that accommodates nonlinear effects in mechanical systems without taking any approximation. Invoking the tools of differential geometry, a Z-valued quantity in terms of a topological index in differential geometry known as the Poincaré-Hopf index, which features the topological invariant of nonlinear 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 nonlinear ZMs in the future.

Citations

• Z2classification of quantum spin Hall systems: An approach using time-reversal invariance
• Nonlinear conduction via solitons in a topological mechanical insulator
• Topological modes bound to dislocations in mechanical metamaterials
• Topological Insulators with Inversion Symmetry
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Topological Insulators
• Topological Edge Floppy Modes in Disordered Fiber Networks
• Fracturing of topological Maxwell lattices