Fully-Polarized Topological Isostatic Metamaterials in Three Dimensions

TL;DR

This paper introduces fully-polarized topological mechanical phases in three-dimensional isostatic lattices, demonstrating their unique surface states and tunable properties through theoretical and experimental methods, advancing the design of adaptive metamaterials.

Contribution

It presents the first realization of fully-polarized topological mechanical phases in 3D, free of Weyl lines, with experimental validation and tunable surface floppy modes.

Findings

Surface floppy modes are fully polarized on specific boundaries.

Weyl lines disrupt polarization in 3D lattices.

Soft strains can reversibly switch between topological phases.

Abstract

Topological surface states are unique to topological materials and are immune to disturbances. In isostatic lattices, mechanical topological floppy modes exhibit softness depending on the polarization relative to the terminating surface. However, in three dimensions, the polarization of topological floppy modes is disrupted by the ubiquitous mechanical Weyl lines. Here, we demonstrate, both theoretically and experimentally, the fully-polarized topological mechanical phases free of Weyl lines. Floppy modes emerge exclusively on a particular surface of the three-dimensional isostatic structure, leading to the strongly asymmetric stiffness between opposing boundaries. Additionally, uniform soft strains can reversibly shift the lattice configuration to Weyl phases, reducing the stiffness contrast to a trivially comparable level. Our work demonstrates the fully-polarized topological mechanical phases in three dimensions, and paves the way towards engineering soft and adaptive metamaterials.