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 language | English (US) |
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Pages (from-to) | 695-717 |
Number of pages | 23 |
Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Volume | 467 |
Issue number | 2127 |
DOIs | |
State | Published - Mar 8 2011 |
Keywords
- Linear elasticity
- Phase transformation
- Precipitate
ASJC Scopus subject areas
- General Mathematics
- General Engineering
- General Physics and Astronomy