Programmable and robust static topological solitons in mechanical metamaterials

Yafei Zhang,Bo Li,Guy M Genin,Q S Zheng,C Q Chen

doi:10.1038/s41467-019-13546-y

Yafei Zhang, Bo Li + Show 3 more

Open Access

https://doi.org/10.1038/s41467-019-13546-y

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Abstract

Solitary, persistent wave packets called solitons hold potential to transfer information and energy across a wide range of spatial and temporal scales in physical, chemical, and biological systems. Mechanical solitons characteristically emerge either as a single wave packet or uncorrelated propagating topological entities through space and/or time, but these are notoriously difficult to control. Here, we report a theoretical framework for programming static periodic topological solitons into a metamaterial, and demonstrate its implementation in real metamaterials computationally and experimentally. The solitons are excited by deformation localizations under quasi-static compression, and arise from buckling-induced kink-antikink bands that provide domain separation barriers. The soliton number and wavelength demonstrate a previously unreported size-dependence, due to intrinsic length scales. We identify that these unanticipated solitons stem from displacive phase transitions with periodic topological excitations captured by the well-known {varphi }^{4} theory. Results reveal pathways for robust regularizations of stochastic responses of metamaterials.

Highlights

Solitary, persistent wave packets called solitons hold potential to transfer information and energy across a wide range of spatial and temporal scales in physical, chemical, and biological systems
Inspired by recent numerical work indicating that excitations of ordered localizations can be achieved via carefully designed architectures[30], here we develop a general framework for analyzing this entire class of materials through the formalism of static periodic solitons
Beyond a critical loading, deformation symmetry breaks down, leading to two distinct macroscopic buckling modes separated by localized topological interfaces that are static periodic solitons governed by the well-known φ4 equation[33,34]

Summary

Introduction

Persistent wave packets called solitons hold potential to transfer information and energy across a wide range of spatial and temporal scales in physical, chemical, and biological systems. Both experiments and simulations show that the macroscopic buckling and localized deformation in the metamaterial seem to be insensitive to the number of unit cells in the vertical direction We measure the characteristic angle θ of the samples in experiments and simulations by calculating the averaged relative rotations of the point pairs, marked on the vertical necks of each cell in the middle row (see Supplementary Fig. 2).

Results

Conclusion