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MiS Preprint

A constrained theory of magnetoelasticity

Antonio DeSimone and Richard D. James


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 Tb0.3 Dy0.7 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.

Nov 14, 2000
Nov 14, 2000
magnetoelastic material, microstructures, phase transformation, sensors and actuators, variational calculus

Related publications

2002 Repository Open Access
Antonio DeSimone and Richard D. James

A constrained theory of magnetoelasticity

In: Journal of the mechanics and physics of solids, 50 (2002) 2, pp. 283-320