DeSimone, Antonio Hysteresis and imperfection sensitivity in small ferromagnetic particles. (English) Zbl 0836.73060 Meccanica 30, No. 5, 591-603 (1995). Summary: The classical results of E. C. Stoner and E. P. Wohlfarth [Philos. Trans. R. Soc. Lond., Ser. A 240, 599–644 (1948)] for the prediction of hysteresis loops in small ferromagnetic particles are extended to specimens of non-ellipsoidal shape, and shown to be a consequence of micromagnetics. The insensitivity to surface roughness is proposed as a possible explanation of the high coercivity behavior of small particles. Cited in 20 Documents MSC: 74A60 Micromechanical theories 74M25 Micromechanics of solids 74S30 Other numerical methods in solid mechanics (MSC2010) 74P10 Optimization of other properties in solid mechanics 82D40 Statistical mechanics of magnetic materials Keywords:local minimizers; phase transformations; specimens of non-ellipsoidal shape; micromagnetics; high coercivity PDFBibTeX XMLCite \textit{A. DeSimone}, Meccanica 30, No. 5, 591--603 (1995; Zbl 0836.73060) Full Text: DOI References: [1] Aharoni, A. ?Perfect and imperfect particles?,IEEE Trans. Magn.,22 (1986) 478-483. · doi:10.1109/TMAG.1986.1064461 [2] Anzellotti, G. and Baldo, S., ?Asymptotic development by ?-convergence?, Preprint (1990). · Zbl 0780.49011 [3] Ball, J.M. and James, R.D., ?Proposed experimental tests of a theory of fime microstructure and the two-well problem?,Phil. Trans. Roy. Soc.,A338 (1992) 389-450. · Zbl 0758.73009 [4] Brown, W.F. ?Virtues and weaknesses of the domain concept?,Revs. Mod. Phys.,17 (1945) 15-19. · doi:10.1103/RevModPhys.17.15 [5] Brown, W.F.Micromagnetics, John Wiley and Sons (Interscience), 1963. [6] Dal Maso, G.An Introduction to ?-Convergence, Birkhäuser, 1993. [7] De Giorgi, E. and Franzoni, T., ?Su un tipo di convergenza variazionale?,Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.,68 (1975) 842-850. [8] DeSimone, A. ?Energy minimizers for large ferromagnetic bodies?,Arch. Rat. Mech. Anal.,125 (1993) 99-143. · Zbl 0811.49030 · doi:10.1007/BF00376811 [9] DeSimone, A. ?The effect of applied loads on the magnetostrictive response of a Terfenol-D-type material: a micromagnetic analysis?, Scripta Met., in press (1995). [10] Jakubovics, J.P.,Magnetism and Magnetic Materials, The Institute of Metals, 1987. [11] James R.D. and Kinderlehrer D., ?Frustration in ferromagnetic materials?,Cont. Mech. Thermodyn.,2 (1990) 215-239. · doi:10.1007/BF01129598 [12] James R.D. and Kinderlehrer D., ?Theory of magnetostriction with applications to Tb x Dy1?x Fe2?,Phil. Mag.,B68 (1993) 237-274. [13] Kohn R.V., ?The relaxation of a double well energy?,Cont. Mech. Thermodyn.,3 (1991) 193-236. · Zbl 0825.73029 · doi:10.1007/BF01135336 [14] Kohn, R.V. and Sternberg, P., ?Local minimisers and singular perturbations?,Proc. Roy. Soc. Edinburgh,111A (1989) 69-84. · Zbl 0676.49011 [15] Néel, L. ?Influence des fluctuation thermiques sur l’aimantation de grains ferromagnétiques très fins?,Compt. Rend.,228 (1949), 664-666. [16] Stoner, E.C. and Wohlfarth, E.P., ?A mechanism of magnetic hysteresis in heterogeneous alloys?,Proc. Roy. Soc. London,240A (1948) 599-642. · Zbl 0031.38003 [17] Visintin, A., ?On Landau-Lifshitz equations for ferromagnetism?,Jap. J. Appl. Math.,2 (1985) 69-84. · Zbl 0613.35018 · doi:10.1007/BF03167039 [18] Zijlstra, H., ?Permanent magnets: theory?, inFerromagnetic Materials, Vol. 3, edited by Wohlfarth, E.P., North-Holland, 1985. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.