A theoretical framework for physically-realizable kagome metamaterials and its implications on dualities and topological edge modes

TL;DR

This paper develops a theoretical framework for realistic kagome metamaterials, accounting for structural effects like ligament bending, and explores their dynamic properties, dualities, and topological edge modes, validated through finite element analysis.

Contribution

It introduces a new theoretical model for physically-realizable kagome metamaterials that incorporates structural effects, enabling analysis of their dynamic and topological properties.

Findings

Structural components significantly influence topological edge modes.

The framework predicts conditions for dispersion dualities.

Finite element analysis validates the theoretical predictions.

Abstract

Since the discovery of topological modes in idealized ball-and-spring kagome lattices, significant efforts have been devoted to realizing mechanical analogues of these ideal lattices via practical fabrication techniques. While numerical and experimental characterizations of these mechanical analogues have been reported, theoretical modeling that accounts for realistic structural effects (e.g., the bending behavior of thin ligaments-a departure from ideal hinges allowing free rotation) has been lacking. Here we propose a theoretical framework to investigate the dynamic properties of physically-realizable kagome metamaterials consisting of solid triangles and ligaments, in which triangles and ligaments are modeled as rigid bodies and elastic springs, respectively. By applying the framework, validated through finite element analysis, to twisted and deformed kagome metamaterials, we theoretically show the required conditions for achieving certain unique dynamic properties, including dispersion dualities and topological edge modes. The presented study unequivocally reveals the effects of structural components on these properties, which could enable new design strategies for wave propagation manipulation in kagome-based metamaterials.