Magnetostrictive composites in the dilute limit

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

We calculate the effective properties of a magnetostrictive composite in the dilute limit. The composite consists of well separated identical ellipsoidal particles of magnetostrictive material, surrounded by an elastic matrix. The free energy of the magnetostrictive particles is computed using the constrained theory of DeSimone and James [2002. A constrained theory of magnetoelasticity with applications to magnetic shape memory materials. J. Mech. Phys. Solids 50, 283-320], where application of an external field causes rearrangement of variants rather than rotation of the magnetization or elastic strain in a variant. The free energy of the composite has an elastic energy term associated with the deformation of the surrounding matrix and demagnetization terms. By using results from the constrained theory and from the Eshelby inclusion problem in linear elasticity, we show that the energy minimization problem for the composite can be cast as a quadratic programming problem. The solution of the quadratic programming problem yields the effective properties of Ni2MnGa and Terfenol-D composite systems. Numerical results show that the average strain of the composite depends strongly on the particle shape, the applied stress, and the elastic modulus of the matrix.

Original languageEnglish (US)
Pages (from-to)951-974
Number of pages24
JournalJournal of the Mechanics and Physics of Solids
Volume54
Issue number5
DOIs
StatePublished - May 1 2006

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composite materials
Composite materials
quadratic programming
Quadratic programming
Free energy
matrices
Demagnetization
free energy
Shape memory effect
demagnetization
Large scale systems
Elasticity
magnetostriction
Magnetization
Elastic moduli
casts
modulus of elasticity
elastic properties
inclusions
magnetization

Keywords

  • Constrained theory
  • Eshelby problem
  • Magnetostrictive composite

Cite this

Magnetostrictive composites in the dilute limit. / Liu, L. P.; James, Richard D; Leo, Perry H.

In: Journal of the Mechanics and Physics of Solids, Vol. 54, No. 5, 01.05.2006, p. 951-974.

Research output: Contribution to journalArticle

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AB - We calculate the effective properties of a magnetostrictive composite in the dilute limit. The composite consists of well separated identical ellipsoidal particles of magnetostrictive material, surrounded by an elastic matrix. The free energy of the magnetostrictive particles is computed using the constrained theory of DeSimone and James [2002. A constrained theory of magnetoelasticity with applications to magnetic shape memory materials. J. Mech. Phys. Solids 50, 283-320], where application of an external field causes rearrangement of variants rather than rotation of the magnetization or elastic strain in a variant. The free energy of the composite has an elastic energy term associated with the deformation of the surrounding matrix and demagnetization terms. By using results from the constrained theory and from the Eshelby inclusion problem in linear elasticity, we show that the energy minimization problem for the composite can be cast as a quadratic programming problem. The solution of the quadratic programming problem yields the effective properties of Ni2MnGa and Terfenol-D composite systems. Numerical results show that the average strain of the composite depends strongly on the particle shape, the applied stress, and the elastic modulus of the matrix.

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