Localizing softness and stress along loops in 3D topological metamaterials

Guido Baardink, Anton Souslov, Jayson Paulose, Vincenzo Vitelli

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Topological states can be used to control the mechanical properties of a material along an edge or around a localized defect. The rigidity of elastic networks is characterized by a topological invariant called the polarization; materials with a well-defined uniform polarization display a dramatic range of edge softness depending on the orientation of the polarization relative to the terminating surface. However, in all 3D mechanical metamaterials proposed to date, the topological modes are mixed with bulk soft modes, which organize themselves in Weyl loops. Here, we report the design of a 3D topological metamaterial without Weyl lines and with a uniform polarization that leads to an asymmetry between the number of soft modes on opposing surfaces. We then use this construction to localize topological soft modes in interior regions of the material by including defect lines-dislocation loops-that are unique to three dimensions. We derive a general formula that relates the difference in the number of soft modes and states of self-stress localized along the dislocation loop to the handedness of the vector triad formed by the lattice polarization, Burgers vector, and dislocation-line direction. Our findings suggest a strategy for preprogramming failure and softness localized along lines in 3D, while avoiding extended soft Weyl modes.

Original languageEnglish
Pages (from-to)489-494
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number3
Early online date28 Dec 2017
Publication statusPublished - 16 Jan 2018

ASJC Scopus subject areas

  • General


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