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 Tb0.3Dy0.7Fe2. 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.
Bibliographical noteFunding Information:
Part of this research was conducted while ADS was enjoying the hospitality of the Department of Aerospace Engineering and Mechanics at the University of Minnesota as a Visiting Professor for Research. Fruitful discussions with S. Müller are gratefully acknowledged. The authors would also like to thank ONR (N00014-99-1-0925 and N00014-95-1-1145), AFOSR/MURI (F49620-98-1-0433), ARO (DAAG55-98-1-0335) and NSF (DMS-0074043) for supporting this work.
- A. Microstructures
- B. Magnetoelastic material
- C. Energy methods