### 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 language | English (US) |
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Pages (from-to) | 951-974 |

Number of pages | 24 |

Journal | Journal of the Mechanics and Physics of Solids |

Volume | 54 |

Issue number | 5 |

DOIs | |

State | Published - May 1 2006 |

### Fingerprint

### Keywords

- Constrained theory
- Eshelby problem
- Magnetostrictive composite

### Cite this

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

Research output: Contribution to journal › Article

*Journal of the Mechanics and Physics of Solids*, vol. 54, no. 5, pp. 951-974. https://doi.org/10.1016/j.jmps.2005.11.006

}

TY - JOUR

T1 - Magnetostrictive composites in the dilute limit

AU - Liu, L. P.

AU - James, Richard D

AU - Leo, Perry H

PY - 2006/5/1

Y1 - 2006/5/1

N2 - 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.

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.

KW - Constrained theory

KW - Eshelby problem

KW - Magnetostrictive composite

UR - http://www.scopus.com/inward/record.url?scp=32444444940&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=32444444940&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2005.11.006

DO - 10.1016/j.jmps.2005.11.006

M3 - Article

AN - SCOPUS:32444444940

VL - 54

SP - 951

EP - 974

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

IS - 5

ER -