• DOI:10.1073/pnas.1502939112
• Corpus ID: 2402181

Selective buckling via states of self-stress in topological metamaterials

@article{Paulose2015SelectiveBV,
  title={Selective buckling via states of self-stress in topological metamaterials},
  author={Jayson Paulose and Anne S. Meeussen and Vincenzo Vitelli},
  journal={Proceedings of the National Academy of Sciences},
  year={2015},
  volume={112},
  pages={7639 - 7644}
}

• J. Paulose, A. S. Meeussen, V. Vitelli
• Published 11 February 2015
• Engineering
• Proceedings of the National Academy of Sciences

Significance An ongoing challenge in modern materials science is to create artificial structures, termed metamaterials, with an unconventional response that can be programmed by suitable design of their geometry or topology. We demonstrate a novel metamaterial in which small structural variations single out regions that buckle selectively under external stresses. Surprisingly, these regions are at first glance indistinguishable from the rest of the structure. Our samples are examples of topological metamaterials that are the mechanical analogues of topologically protected electronic systems. As a result, the buckling response is robust against structural perturbations yet tunable without affecting secondary physical properties in the buckling region. This feature is desirable for optomechanical or thermomechanical metamaterials in which multiple characteristics need to be tuned simultaneously. 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.