Microstructural models of magnetostrictive materials

Deborah Brandon; Robert C. Rogers

doi:10.1117/12.148401

22 July 1993 Microstructural models of magnetostrictive materials

Deborah Brandon, Robert C. Rogers

Proceedings Volume 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures; (1993) https://doi.org/10.1117/12.148401
Event: 1993 North American Conference on Smart Structures and Materials, 1993, Albuquerque, NM, United States

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 Tb_xDy_(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.

Citation Download Citation

Deborah Brandon and Robert C. Rogers "Microstructural models of magnetostrictive materials", Proc. SPIE 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures, (22 July 1993); https://doi.org/10.1117/12.148401

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