Selective buckling via states of self-stress in topological metamaterials

States of self-stress—tensions and compressions of structural elements that result in zero net forces—play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable mechanical properties. We exploit a class of recently introduced state...

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Published inProceedings of the National Academy of Sciences - PNAS Vol. 112; no. 25; pp. 7639 - 7644
Main Authors Paulose, Jayson, Meeussen, Anne S., Vitelli, Vincenzo
Format Journal Article
LanguageEnglish
Published United States National Academy of Sciences 23.06.2015
National Acad Sciences
Subjects
Mechanical properties
Physical Sciences
Quantum physics
Topology
isostatic lattices
topological modes
tunable failure
topological mechanics
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Summary:States of self-stress—tensions and compressions of structural elements that result in zero net forces—play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable mechanical properties. We exploit a class of recently introduced states of self-stress analogous to topological quantum states to sculpt localized buckling regions in the interior of periodic cellular metamaterials. Although the topological states of self-stress arise in the linear response of an idealized mechanical frame of harmonic springs connected by freely hinged joints, they leave a distinct signature in the nonlinear buckling behavior of a cellular material built out of elastic beams with rigid joints. The salient feature of these localized buckling regions is that they are indistinguishable from their surroundings as far as material parameters or connectivity of their constituent elements are concerned. Furthermore, they are robust against a wide range of structural perturbations. We demonstrate the effectiveness of this topological design through analytical and numerical calculations as well as buckling experiments performed on two- and three-dimensional metamaterials built out of stacked kagome lattices.
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Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved May 11, 2015 (received for review February 13, 2015)
Author contributions: J.P., A.S.M., and V.V. designed research; J.P. and A.S.M. performed research; J.P., A.S.M., and V.V. contributed new reagents/analytic tools; J.P. and A.S.M. analyzed data; and J.P., A.S.M., and V.V. wrote the paper.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1502939112