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Symmetry breaking in indented elastic cones
https://doi.org/10.1142/S0218202517500026Cited by:7 (Source: Crossref)
Abstract
Motivated by simulations of carbon nanocones (see [S. P. Jordan and V. H. Crespi, Theory of carbon nanocones: Mechanical chiral inversion of a micron-scale three-dimensional object, Phys. Rev. Lett.93 (2004) 255504]), 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 Kármán 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 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.
Communicated by I. Fonseca
AMSC: 49Q10, 74K20
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