Topological Directional Response in the Continuum Limit of Mechanical Metamaterials
Abstract
Flexible mechanical metamaterials display an exciting variety of novel deformation properties, including programmability, nonlinearity and robustness. However, these functionalities, which rely on nonuniform deformations of the microscopic unit cell of which the metamaterial is composed, are not captured by conventional elastic theory, creating a challenge in examining their actual large-scale properties. We address this via micromorphic continuum elasticity, which treats deformations that are nonuniform locally yet vary smoothly over larger lengthscales. We examine in particular topological edge and interface modes and directional response analogous to that observed by Kane and Lubensky in discrete models. We identify a new counting argument between modes of deformation and constraints that ensures mechanical criticality in the continuum, leading to a novel correspondence between a bulk topological invariant and boundary modes. Finally, we explore the lengthscales of deformations governed by this theory for given system geometries, elastic properties and disorder.
- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- 2019
- Bibcode:
- 2019APS..MARX57010S