Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

Ray W Ogden

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.
Original languageEnglish
Pages (from-to)570-580
Number of pages11
JournalInternational Journal of Non-Linear Mechanics
Volume44
Issue number5
Early online date6 Dec 2008
DOIs
Publication statusPublished - Jun 2009

Fingerprint

Finite Deformation
Electromagnetic fields
Electromagnetic Fields
Motion
Wave Speed
Magnetic fields
Governing equation
Shear waves
Magnetic Field
Wave propagation
Configuration
Approximation
Electric fields
Acoustic waves
Plane Wave
Wave Propagation
Electric Field
Acoustics
Harmonic
Disturbance

Keywords

  • non-linear magnetoelasticity
  • non-linear electroelasticity
  • incremental notions
  • finite deformations
  • continuum electrodynamics

Cite this

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field. / Ogden, Ray W.

In: International Journal of Non-Linear Mechanics, Vol. 44, No. 5, 06.2009, p. 570-580.

Research output: Contribution to journalArticle

@article{b04e6516c9434608a3df7a4ac22a62f0,
title = "Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field",
abstract = "The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.",
keywords = "non-linear magnetoelasticity, non-linear electroelasticity, incremental notions, finite deformations, continuum electrodynamics",
author = "Ogden, {Ray W}",
year = "2009",
month = "6",
doi = "10.1016/j.ijnonlinmec.2008.11.017",
language = "English",
volume = "44",
pages = "570--580",
journal = "International Journal of Non-Linear Mechanics",
issn = "0020-7462",
publisher = "Elsevier Limited",
number = "5",

}

TY - JOUR

T1 - Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

AU - Ogden, Ray W

PY - 2009/6

Y1 - 2009/6

N2 - The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.

AB - The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.

KW - non-linear magnetoelasticity

KW - non-linear electroelasticity

KW - incremental notions

KW - finite deformations

KW - continuum electrodynamics

U2 - 10.1016/j.ijnonlinmec.2008.11.017

DO - 10.1016/j.ijnonlinmec.2008.11.017

M3 - Article

VL - 44

SP - 570

EP - 580

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

IS - 5

ER -