  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 behaviour 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.
