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.