Existence of energy minimizers for magnetostrictive materials

Piotr Rybka; Mitchell Luskin

doi:10.1137/S0036141004442021

Existence of energy minimizers for magnetostrictive materials

Piotr Rybka, Mitchell Luskin

School of Mathematics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

The existence of a deformation and magnetization minimizing the magnetostrictive free energy is given. Mathematical challenges are presented by a free energy that includes elastic contributions defined in the reference configuration and magnetic contributions defined in the spatial frame. The one-to-one a.e. and orientation-preserving property of the deformation is demonstrated, and the satisfaction of the nonconvex saturation constraint for the magnetization is proven.

Original language	English (US)
Pages (from-to)	2004-2019
Number of pages	16
Journal	SIAM Journal on Mathematical Analysis
Volume	36
Issue number	6
DOIs	https://doi.org/10.1137/S0036141004442021
State	Published - 2005

Keywords

Calculus of variations
Magnetostriction
Micromagnetics

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10.1137/S0036141004442021

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abstract = "The existence of a deformation and magnetization minimizing the magnetostrictive free energy is given. Mathematical challenges are presented by a free energy that includes elastic contributions defined in the reference configuration and magnetic contributions defined in the spatial frame. The one-to-one a.e. and orientation-preserving property of the deformation is demonstrated, and the satisfaction of the nonconvex saturation constraint for the magnetization is proven.",

keywords = "Calculus of variations, Magnetostriction, Micromagnetics",

author = "Piotr Rybka and Mitchell Luskin",

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AU - Luskin, Mitchell

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AB - The existence of a deformation and magnetization minimizing the magnetostrictive free energy is given. Mathematical challenges are presented by a free energy that includes elastic contributions defined in the reference configuration and magnetic contributions defined in the spatial frame. The one-to-one a.e. and orientation-preserving property of the deformation is demonstrated, and the satisfaction of the nonconvex saturation constraint for the magnetization is proven.

KW - Calculus of variations

KW - Magnetostriction

KW - Micromagnetics

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 6

ER -

Existence of energy minimizers for magnetostrictive materials

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