Magnetostatics: from Basic Principles to Nonlinear Interactions in Deformable Media

Raymond William Ogden

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

In these notes we provide a development of the basic principles of the classical theory of magnetostatics, from the fundamental notions of magnetic dipoles through to distributions of current in a non-deformable continuum, the equations governing the magnetic field and magnetic induction vectors in free space and in a magnetizable material, and then to the modifications of the theory required to account for the deformability of material media. A review of the relevant continuum mechanics is included as a prelude to the description of large magnetoelastic deformations. The constitutive equations for a nonlinear magnetoelastic material are presented first in Eulerian form and then an alternative formulation of the equations based on a Lagrangian approach is adopted, which leads to an elegant and relatively simple structure for the constitutive equations and the governing differential equations. The theory is specialized further to the case of an isotropic magnetoelastic material and representative prototype boundary-value problems are formulated and then solved using a simple model constitutive law in order to illustrate the nonlinear magnetoelastic coupling.
Original languageEnglish
Title of host publicationMechanics and Electrodynamics of Magneto- and Electro-elastic Materials
EditorsRaymond Ogden, David Steigmann
Place of PublicationVienna, Austria
PublisherSpringer
Pages107-152
Number of pages46
ISBN (Print)978-3709107003
DOIs
Publication statusPublished - 7 Apr 2011

Publication series

NameCISM International Centre for Mechanical Sciences - Courses and Lectures
PublisherSpringer
Volume527
ISSN (Print)0254-1971

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constitutive equations
magnetostatics
continuum mechanics
magnetic induction
magnetic dipoles
boundary value problems
induction
differential equations
prototypes
interactions
continuums
formulations
magnetic fields

Cite this

Ogden, R. W. (2011). Magnetostatics: from Basic Principles to Nonlinear Interactions in Deformable Media . In R. Ogden, & D. Steigmann (Eds.), Mechanics and Electrodynamics of Magneto- and Electro-elastic Materials (pp. 107-152). (CISM International Centre for Mechanical Sciences - Courses and Lectures; Vol. 527). Vienna, Austria: Springer . https://doi.org/10.1007/978-3-7091-0701-0_3

Magnetostatics : from Basic Principles to Nonlinear Interactions in Deformable Media . / Ogden, Raymond William.

Mechanics and Electrodynamics of Magneto- and Electro-elastic Materials. ed. / Raymond Ogden; David Steigmann. Vienna, Austria : Springer , 2011. p. 107-152 (CISM International Centre for Mechanical Sciences - Courses and Lectures; Vol. 527).

Research output: Chapter in Book/Report/Conference proceedingChapter

Ogden, RW 2011, Magnetostatics: from Basic Principles to Nonlinear Interactions in Deformable Media . in R Ogden & D Steigmann (eds), Mechanics and Electrodynamics of Magneto- and Electro-elastic Materials. CISM International Centre for Mechanical Sciences - Courses and Lectures, vol. 527, Springer , Vienna, Austria, pp. 107-152. https://doi.org/10.1007/978-3-7091-0701-0_3
Ogden RW. Magnetostatics: from Basic Principles to Nonlinear Interactions in Deformable Media . In Ogden R, Steigmann D, editors, Mechanics and Electrodynamics of Magneto- and Electro-elastic Materials. Vienna, Austria: Springer . 2011. p. 107-152. (CISM International Centre for Mechanical Sciences - Courses and Lectures). https://doi.org/10.1007/978-3-7091-0701-0_3
Ogden, Raymond William. / Magnetostatics : from Basic Principles to Nonlinear Interactions in Deformable Media . Mechanics and Electrodynamics of Magneto- and Electro-elastic Materials. editor / Raymond Ogden ; David Steigmann. Vienna, Austria : Springer , 2011. pp. 107-152 (CISM International Centre for Mechanical Sciences - Courses and Lectures).
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