Mechanical properties of topological metamaterials

Abstract

Recent advances in physics and engineering have led to the discovery of behavioral correlations between thermal, electromagnetic, optical, quantum and classical mechanical metamaterial systems. Of particular interest for the development of novel metamaterial properties is topological polarization, a new mapping established between quantum mechanical topological insulators and mechanical systems. Although recent research has shown many properties of polarized regions in metamaterials, the relationship between the topological effects, force concentration along domain boundaries, and mechanical properties of polarized lattices has found little attention. Further, current findings are also limited to linear continuous boundary regions. Here, we show how the hexagonal Kagome lattice and square lattice in their polarized state can concentrate axial forces along non-linear boundary regions and how the resulting mechanical properties depend on both the direction of the external loading and the magnitude of the nodal displacements used to polarize the given lattices. The results show that the mechanical properties of polarized lattices are primarily informed by the switch from a stretch-dominated to a bending-dominated state during polarization, but also by the increasing force concentration in the domain boundaries. These findings enable the design of complex topological lattices with predetermined concentration behavior while also accounting for changes in the overall mechanical properties.