Minimal energy for elastic inclusions

Hans Knüpfer, Robert Kohn

Research output: Contribution to journalArticle

Abstract

We consider a variant of the isoperimetric problem with a non-local term representingelastic energy. More precisely, our aim is to analyse the optimal energy of an inclusion of a fixed volume the energy of which is determined by surface and elastic energies. This problem has been studied extensively in the physical/metallurgical literature; however, the analysis has mainly been either (i) numerical, or (ii) restricted to a specific set of inclusion shapes, e.g. ellipsoids. In this article, we prove a lower bound for the energy, with no a priori hypothesis on the shape (or even number) of the inclusions. This journal is

Original languageEnglish (US)
Pages (from-to)695-717
Number of pages23
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume467
Issue number2127
DOIs
StatePublished - Mar 8 2011

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Minimal Energy
Inclusion
inclusions
Energy
isoperimetric problem
energy
Isoperimetric Problem
Even number
Ellipsoid
ellipsoids
surface energy
Lower bound
Term

Keywords

  • Linear elasticity
  • Phase transformation
  • Precipitate

ASJC Scopus subject areas

  • Engineering(all)
  • Mathematics(all)
  • Physics and Astronomy(all)

Cite this

Minimal energy for elastic inclusions. / Knüpfer, Hans; Kohn, Robert.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 467, No. 2127, 08.03.2011, p. 695-717.

Research output: Contribution to journalArticle

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