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Topological defects produce exotic mechanics in complex metamaterials


The basic tenet of metamaterials is that the architecture controls the physics1,2,3,4,5,6,7,8,9,10,11,12. So far, most studies have considered defect-free architectures. However, defects, and particularly topological defects, play a crucial role in natural materials13,14,15. Here we provide a systematic strategy for introducing such defects in mechanical metamaterials. We first present metamaterials that are a mechanical analogue of spin systems with tunable ferromagnetic and antiferromagnetic interactions, then design an exponential number of frustration-free metamaterials and finally introduce topological defects by rotating a string of building blocks in these metamaterials. We uncover the distinct mechanical signature of topological defects using experiments and simulations, and leverage this to design complex metamaterials in which external forces steer deformations and stresses towards complementary parts of the system. Our work presents a new avenue to systematically including spatial complexity, frustration and topology in mechanical metamaterials.

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Fig. 1: Designing structurally complex, compatible metamaterials.
Fig. 2: Defect design in periodic and complex metamaterials.
Fig. 3: Mechanical detection of defects.
Fig. 4: Forcing pairs of building blocks steers stresses and deformations.

Data availability

The data represented in Fig. 1h and Fig. 3b–e are provided with the paper as source data. All other data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

Code availability

The code that supports the plots within this paper and other findings of this study is available from the corresponding author on reasonable request.


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We thank R. Ilan, E. Lerner, B. Mulder, B. Pisanty, E. Teomy and E. Verhagen for fruitful discussions, J. Paulose for co-developing code for the numerical model FH, D. Ursem for technical support and R. Zandbergen for supplying the exact counting data in Fig. 1h. This research was supported in part by the Israel Science Foundation grant no. 968/16.

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Authors and Affiliations



M.v.H and Y.S. conceived the project. E.C.O. conceived the structural characterization of defects. A.S.M. conceived the mechanical detection of defects. A.S.M. and E.C.O performed simulations. A.S.M. performed experiments. All authors contributed to the analysis of the results and to the writing of the manuscript.

Corresponding author

Correspondence to Anne S. Meeussen.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Cristiano Nisoli and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–6 and captions.

Source data

Source Data Fig. 1

Numerical data used to generate Fig.1h.

Source Data Fig. 3

Numerical data used to generate Fig.3b–e.

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Meeussen, A.S., Oğuz, E.C., Shokef, Y. et al. Topological defects produce exotic mechanics in complex metamaterials. Nat. Phys. 16, 307–311 (2020).

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