Symmetry breaking in indented elastic cones
Heiner Olbermann (Bonn)
Abstract: Motivated by simulations of carbon nanocones (see Jordan and Crespi, Phys. Rev. Lett., 2004),
we consider a variational plate model for an elastic cone under compression in the direction of the cone
symmetry axis. Assuming radial symmetry, and modeling the compression by suitable Dirichlet boundary
conditions at the center and the boundary of the sheet, we identify the energy scaling law in the von-Karman plate model.
Specifically, we find that three different regimes arise with increasing indentation: initially the energetic cost of the
logarithmic singularity dominates, then there is a linear response corresponding to a moderate deformation close
to the boundary of the cone, and for larger indentation a localized inversion takes place in the central region.
Then we show that for large enough indentations minimizers of the elastic energy cannot be radially symmetric.
We do so by an explicit construction that achieves lower elastic energy than the minimum amount possible for
radially symmetric deformations.