Two-dimensional microtwist modeling of topological polarization in hinged Kagome lattices and its experimental validation

Abstract

Kagome lattices have recently attracted a great attention because of the unique mechanical properties including their topological polarization and localized zero modes at certain edges, which challenge the standard effective continuum theories. The previous study of these systems has been predominantly focused on the ideal Kagome lattice with the spring–mass models. In this study, we stretch this paradigm by exploring the hinged Kagome lattices towards practical application to understand the topological polarization under the framework of the microtwist continuum. The hinges are modeled by ligaments capable of supporting stretching, shear and bending deformations. The microtwist elasticity is then formulated thanks to leading order two-scale asymptotics and its constitutive and balance equations are derived. Performance of the proposed theory is validated by the exact solution for predicting dispersion relations and periodic zero modes. We further demonstrate the effectiveness of this theory through numerical simulations as well as experimental testing. Finally, nonuniform deformation under complex loadings and parity asymmetric surface waves in microtwist media are explored. Our study provides a great potential of using the microtwist medium to design, control and program hinge-based metamaterials.