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Bibliographic Details
Main Authors: Akramov, Ibrokhimbek, Knüpfer, Hans, Kružík, Martin, Rüland, Angkana
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2207.13746
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Table of Contents:
  • We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion of a fixed volume for which the energy is determined by a surface and an (anisotropic) elastic contribution. Following ideas from \cite{CS} and \cite{KnuepferKohn-2011}, we derive the lower scaling bound by invoking a two-well rigidity argument and a covering result. The upper bound follows from a well-known construction for a lens-shaped elastic inclusion.