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Energy Scaling Law for a Single Disclination in a Thin Elastic Sheet

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Abstract

We consider a single disclination in a thin elastic sheet of thickness h. We prove ansatz-free lower bounds for the free elastic energy in three different settings: first, for a geometrically fully non-linear plate model; second, for three-dimensional nonlinear elasticity; and third, for the Föppl-von Kármán plate theory. The lower bounds in the first and third result are optimal in the sense that we find upper bounds that are identical to the respective lower bounds in the leading order of h.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Leipzig, Postfach 100920, 04009, Leipzig, Germany

    Heiner Olbermann

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  1. Heiner Olbermann
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Correspondence to Heiner Olbermann.

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Communicated by F. Otto

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Olbermann, H. Energy Scaling Law for a Single Disclination in a Thin Elastic Sheet. Arch Rational Mech Anal 224, 985–1019 (2017). https://doi.org/10.1007/s00205-017-1093-4

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