On variational formulations in nonlinear magnetoelastostatics

Roger Bustamante, Alois Dorfmann, Raymond William Ogden

Research output: Contribution to journalArticle

58 Citations (Scopus)

Abstract

Two new variational principles for nonlinear magnetoelastostatics are derived. Each is based on use of two independent variables: the deformation function and, in one case the scalar magnetostatic potential, in the other the magnetostatic vector potential. The derivations are facilitated by use of Lagrangian magnetic field variables and constitutive laws expressed in terms of these variables. In each case all the relevant governing equations, boundary and continuity conditions emerge. These principles have a relatively simple structure and therefore offer the prospect of leading to finite-element formulations that can be used in the solution of realistic boundary-value problems.

Original languageEnglish
Pages (from-to)725-745
Number of pages21
JournalMathematics and Mechanics of Solids
Volume13
Issue number8
Early online date10 Sep 2007
DOIs
Publication statusPublished - Nov 2008

Fingerprint

Magnetostatics
Variational Formulation
Boundary value problems
Vector Potential
Constitutive Law
Magnetic fields
Variational Principle
Governing equation
Magnetic Field
Boundary Value Problem
Scalar
Finite Element
Formulation

Keywords

  • magnetoelasticity
  • nonlinear elasticity
  • variational principles
  • smart materials

Cite this

On variational formulations in nonlinear magnetoelastostatics. / Bustamante, Roger; Dorfmann, Alois; Ogden, Raymond William.

In: Mathematics and Mechanics of Solids, Vol. 13, No. 8, 11.2008, p. 725-745.

Research output: Contribution to journalArticle

Bustamante, Roger ; Dorfmann, Alois ; Ogden, Raymond William. / On variational formulations in nonlinear magnetoelastostatics. In: Mathematics and Mechanics of Solids. 2008 ; Vol. 13, No. 8. pp. 725-745.
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