Critical Mechanical Structures: Topological Metamaterials and Robust Mechanisms in Messy Matter

Xiaoming Mao
Physics, University of Michigan

ABSTRACT: Critical mechanical structures are structures at the verge of mechanical instability. These structures are characterized by their floppy modes, which are deformations costing little energy. On the one hand, numerous interesting phenomena in soft matter are governed by the physics of critical mechanical structures, because they capture the critical state between solid and liquid. On the other hand, the design of mechanical metamaterials (i.e., engineered materials that gain their unusual mechanical properties, such as negative Poisson's ratio, from their structures) often rely on floppy modes to realize novel properties, and the floppy modes in this situation are called "mechanisms." Mao focuses on floppy modes in critical mechanical structures that are governed by topological invariants, and are thus called "topological edge modes." Mao proposes a new design principle, for mechanical metamaterials that are transformable between states with dramatically different properties, by manipulating topological states. Because of the topological protection, these floppy modes are highly robust against disorder. Mao also discusses recent work exploring topological floppy modes in aperiodic, messy, systems, such as fiber networks and quasicrystalline tilings, which manifest the power of "topological protection," and may lead to broad applications in biology, physics, and engineering.

Note: Recording not available