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Multiscale analysis and modeling of ...

Liu, Liping.

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Multiscale analysis and modeling of magnetostrictive composites.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Multiscale analysis and modeling of magnetostrictive composites./
Author:	Liu, Liping.
Description:	119 p.
Notes:	Advisers: Richard D. James; Perry H. Leo.
Contained By:	Dissertation Abstracts International67-08B.
Subject:	Engineering, Aerospace. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3230226
ISBN:	9780542835865

Multiscale analysis and modeling of magnetostrictive composites.
Liu, Liping.

Multiscale analysis and modeling of magnetostrictive composites. - 119 p.

Advisers: Richard D. James; Perry H. Leo.

Thesis (Ph.D.)--University of Minnesota, 2006.

We calculate the effective properties of magnetostrictive composites by minimizing the total free-energy of the composite system. The Gamma-convergence method and two-scale convergence method are used to account for the multiple scales of the composite systems. There are two cases. In the first case of dilute limit, the composite consists of well separated identical ellipsoidal particles of magnetostrictive material surrounded by an elastic matrix. By using the constrained theory (DeSimone and James, 2002) and the Eshelby's solution (1957), we show that the energy minimization problem for the composite can be cast as a quadratic programming problem. In the second case of finite volume fraction, we assume fine identical magnetostrictive particles embedded periodically inside the elastic matrix. We successfully derive a homogenized theory for this case. We further show that the energy minimization problem can be again cast as a quadratic programming problem if the shape of the magnetostrictive particles in the periodic cell enjoys the same special property as an ellipsoid does in the infinite space.

ISBN: 9780542835865Subjects--Topical Terms:

1018395
Engineering, Aerospace.

Multiscale analysis and modeling of magnetostrictive composites.
LDR:02890nam 2200301 a 45 001 971917
005 20110927
008 110927s2006 eng d
020 $a 9780542835865
035 $a (UnM)AAI3230226
035 $a AAI3230226
040 $a UnM $c UnM
100 1 $a Liu, Liping. $3 850149
245 1 0 $a Multiscale analysis and modeling of magnetostrictive composites.
300 $a 119 p.
500 $a Advisers: Richard D. James; Perry H. Leo.
500 $a Source: Dissertation Abstracts International, Volume: 67-08, Section: B, page: 4541.
502 $a Thesis (Ph.D.)--University of Minnesota, 2006.
520 $a We calculate the effective properties of magnetostrictive composites by minimizing the total free-energy of the composite system. The Gamma-convergence method and two-scale convergence method are used to account for the multiple scales of the composite systems. There are two cases. In the first case of dilute limit, the composite consists of well separated identical ellipsoidal particles of magnetostrictive material surrounded by an elastic matrix. By using the constrained theory (DeSimone and James, 2002) and the Eshelby's solution (1957), we show that the energy minimization problem for the composite can be cast as a quadratic programming problem. In the second case of finite volume fraction, we assume fine identical magnetostrictive particles embedded periodically inside the elastic matrix. We successfully derive a homogenized theory for this case. We further show that the energy minimization problem can be again cast as a quadratic programming problem if the shape of the magnetostrictive particles in the periodic cell enjoys the same special property as an ellipsoid does in the infinite space.
520 $a Some special shapes/inclusions have played a central role in the modeling of magnetostrictive composites. The existence of these special inclusions can be addressed by a related free-boundary obstacle problem. In this way, we construct the so-called "E-inclusions". In physical terms, E-inclusions have the remarkable property that constant magnetization of the inclusion, subjected to periodic boundary conditions, induces constant magnetic field on the inclusions. These inclusions apparently enjoy many interesting properties with respect to homogenization and energy minimization. For instance, we use them to give new results on (a) explicit optimal bounds of the effective moduli of two-phase composites; (b) energy-minimizing microstructures; and (c) the characterization of the Gtheta-closure of two well-ordered composites.
590 $a School code: 0130.
650 4 $a Engineering, Aerospace. $3 1018395
650 4 $a Mathematics. $3 515831
690 $a 0405
690 $a 0538
710 2 0 $a University of Minnesota. $3 676231
773 0 $t Dissertation Abstracts International $g 67-08B.
790 $a 0130
790 1 0 $a James, Richard D., $e advisor
790 1 0 $a Leo, Perry H., $e advisor
791 $a Ph.D.
792 $a 2006
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3230226