A constrained theory of magnetoelasticity

Antonio DeSimone and Richard D. James

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Submission date: 14. Nov. 2000
Pages: 55
published in: Journal of the mechanics and physics of solids, 50 (2002) 2, p. 283-320 
DOI number (of the published article): 10.1016/S0022-5096(01)00050-3
Bibtex
Keywords and phrases: magnetoelastic material, microstructures, phase transformation, sensors and actuators, variational calculus

Abstract:
A simple variational theory for the macroscopic behavior of materials with high anisotropy is derived rigorously from micromagnetics. The derivation leads to a constrained theory in which the state of strain and magnetization lies very near the `energy wells' on most of the body. When specialized to ellipsoidal specimens and constant applied field and stress, the theory becomes a finite dimensional quadratic programming problem. Streamlined methods for solving this problem are given. The theory is illustrated by a prediction of the magnetoelastic behavior of the giant magnetostrictive material Tb_0.3 Dy_0.7 Fe₂. The theory embodies precisely the assumptions that have been postulated for ideal ferromagnetic shape memory, in which the magnetization stays rigidly attached to the easy axes of a martensitic material in the martensitic phase. More generally, the framework can be viewed as a prototype for the derivation of constrained theories for materials that change phase, and whose free energy density grows steeply away from its minima.