Minimal energy for elastic inclusions

Hans Knüpfer; Robert V. Kohn

doi:10.1098/rspa.2010.0316

Minimal energy for elastic inclusions

Hans Knüpfer, Robert V. Kohn

Mathematics

Research output: Contribution to journal › Article

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)
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	https://doi.org/10.1098/rspa.2010.0316
State	Published - Mar 8 2011

Keywords

Linear elasticity
Phase transformation
Precipitate

ASJC Scopus subject areas

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

Access to Document

10.1098/rspa.2010.0316

Fingerprint Dive into the research topics of 'Minimal energy for elastic inclusions'. Together they form a unique fingerprint.

Cite this

@article{43dcecb42caa4652b67e0d85ba61a79f,

title = "Minimal energy for elastic inclusions",

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",

keywords = "Linear elasticity, Phase transformation, Precipitate",

author = "Hans Kn{\"u}pfer and Kohn, {Robert V.}",

year = "2011",

month = mar,

day = "8",

doi = "10.1098/rspa.2010.0316",

language = "English (US)",

volume = "467",

pages = "695--717",

journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",

issn = "0080-4630",

publisher = "Royal Society of London",

number = "2127",

}

TY - JOUR

T1 - Minimal energy for elastic inclusions

AU - Knüpfer, Hans

AU - Kohn, Robert V.

PY - 2011/3/8

Y1 - 2011/3/8

N2 - 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

AB - 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

KW - Linear elasticity

KW - Phase transformation

KW - Precipitate

UR - http://www.scopus.com/inward/record.url?scp=79952325477&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952325477&partnerID=8YFLogxK

U2 - 10.1098/rspa.2010.0316

DO - 10.1098/rspa.2010.0316

M3 - Article

AN - SCOPUS:79952325477

VL - 467

SP - 695

EP - 717

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 2127

ER -