The macroscopic behavior of magnetostrictive materials results from domain evolu tions occurring at a microscopic scale. We show how to compute virgin magnetization and magneto striction curves by appraising the behavior of the underlying microstructures. Our method hinges on an averaging device (Young measures), which allows us to pass from the microscopic to the macro scopic scale. We take into account the kinematical constraints on the accommodation of elastic effects, and we highlight the role of material symmetry in the selection of energetically optimal microstructures. Finally, we analyze the influence of applied surface tractions on the magnetoelastic response of a magnetostrictive specimen.
Get full access to this article
View all access options for this article.
References
1.
Bozorth, R.M.1951. FerromagnetismVan Nostrand.
2.
Bozorth, R.M.1954. "Magnetostriction and Crystal Anisotropy of Single Crystals of Hexagonal Cobalt", Phys. Rev. , 96(2):311-316.
Clark, A.E.1980. "Magnetostrictive Rare Earth-Fe2 Compounds" , in Ferromagnetic Materials, Vol. I, E. P. Wohlfarth, ed., North-Holland .
6.
Clark, A.E.1992. "High Power Rare Earth Magnetostrictive Materials" , in Recent Advances in Adaptive and Sensory Materials , C. A. Rogers and R. C. Rogers, eds., Technomic Publishing Co., Inc.
7.
DeSimone, A.1993. "Energy Minimizers for Large Ferromagnetic Bodies" , Arch. Rat. Mech. Anal. , 125:99-144.
8.
DeSimone, A.1994.a "The Effect of Applied Loads on the Magnetostrictive Response of a Terfenol-D-Type Material: A Micromagnetic Analysis", submitted to Scripta Metallurgica et Materialia .
9.
DeSimone, A.1994b. "Elastic Deformations Induced by Applied Magnetic Fields" , in preparation.
10.
DeSimone, A., D. Kinderlehrer and L. Ma.1994. In preparation.
11.
James, R.D. and D. Kinderlehrer .1990. "Frustration in Ferromagnetic Materials", Cont. Mech. Therm., 2:215-239.
12.
James, R.D. and D. Kinderlehrer .1993. "A Theory of Magnetostriction with Application to TbDyFe2", Phil. Mag. B, 68(2):237-274.
13.
Lawton, H. and K.H. Stewart.1947. "Magnetization Curves for Ferromagnetic Single Crystals", Proc. Roy. Soc., A193:72-88.
14.
Moffet, M.B., J.M. Powers and A.E. Clark.1991a. "Comparison of Terfenol-D and PZT-4 Power Limitations", J. Ac. Soc. Am. , 90:1184.
15.
Moffet, M.B., A.E. Clark, M. Wun-Fogle, J. Lindberg, J.P. Teter, and E.A. McLaughlin .1991b. "Characterization of Terfenol-D for Magnetostrictive Transducers", J. Ac. Soc. Am. , 89:1448.
16.
Néel, L.1944. "Le Lois de 1'Aimantation et de la Subdivision en Domaines Élémentaires d'un Monocristal de Fer", I-III, J. Phys. Rad., 5:241-251, 265-276.
17.
Tartar, L.1990. "H-Measures: A New Approach for Studying Homogenisation, Oscillations and Concentration Effects in Partial Differential Equations" , Proc. Roy. Soc. Edin., 115A:193-230.
18.
Tartar, L.1992. "On Mathematical Tools for Studying Partial Differential Equations of Continuum Physics: H-Measures and Young Measures", Center for Nonlinear Analysis Research Report 92-NA-002.
19.
Tartar, L.1993. Private communication, September 1993.
