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Proceedings Paper

Microstructural models of magnetostrictive materials
Author(s): Deborah Brandon; Robert C. Rogers
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Paper Abstract

In classical mathematical problems describing magnetostrictive ferromagnetic materials, one seeks a magnetization field m and deformation field y that minimize an energy functional composed of four terms: the field energy, the anisotropy or stored energy, the interaction energy, and the exchange energy. The total energy is minimized subject to boundary conditions on the deformation and a pointwise constraint on the magnitude of the deformation: m equals 1 everywhere in the body. The most important mathematical characteristic of this problem is nonattainment: minimizing sequences may oscillate or chatter, and a classical minimizer of the energy may not exist. This paper deals with a particular class of such problems based on the model for TbxDy(1-x)Fe2 developed by James and Kinderlehrer. We seek minimizers the energy of a spherical body subjected to an applied field h0 that is uniform in space and a dead load generated by a constant tensor T0. Exchange energy is set to zero.

Paper Details

Date Published: 22 July 1993
PDF: 10 pages
Proc. SPIE 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures, (22 July 1993); doi: 10.1117/12.148401
Show Author Affiliations
Deborah Brandon, Carnegie Mellon Univ. (United States)
Robert C. Rogers, Virginia Polytechnic Institute and State Univ. (United States)

Published in SPIE Proceedings Vol. 1919:
Smart Structures and Materials 1993: Mathematics in Smart Structures
H. Thomas Banks, Editor(s)

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