Mesoscopic model for ferromagnets with isotropic hardening

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 56, Issue 1, 2005, Pages 107-135

  Roubicek T ^a,b   Kruzik M ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

Author keywords

Ferromagnetism; Hardening; Hysteresis; Rate independent dissipation; Variational inequalities

Indexed keywords

EID: 12444290978     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-003-2108-6     Document Type: Article

References (43)

1. J. Aktaa, A. von der Weth, A new differential equations-based model for nonlinear history-dependent magnetic behavior. J. Magnetism & Magn. Mater. 212 (2000), 267-272.
2. V. Barbu, T. Precupanu, Convexity nad Optimization in Banach spaces. D. Reidel Publ., Dordrecht, 2nd ed., 1986.
3. A. Bergqvist, Magnetic vector hysteresis model with dry friction-like pinning. Physica B 233 (1997), 342-347.
4. M. Brokate, P. Krejč, H. Schnabel, On uniqueness in evolution quasivariational inequalities. Preprint Zentrum Mathematik, TU München, 2002.
5. W.F. Brown, Jr., Magnetostatic principles in ferromagnetism, Springer, New York, 1966.
6. C. Carstensen, A. Prohl, Numerical analysis of relaxed micromagnetics by penalised finite elements, Num. Math. 90 (2001), 65-99.
7. S. Chikazumi, Physics of Magnetism. J.Wiley, New York, 1964.
8. A. DeSimone, Energy minimizers for large ferromagnetic bodies, Arch. Rat. Mech. Anal. 125 (1993), 99-143.
9. M.A. Effendiev, On compactness of the stable set for rate independent processes. Comm. Pure Appl. Math. 2 (2003), 495-509.
10. R. Hill, A variational principle of maximum plastic work in classical plasticity. Q.J. Mech. Appl. Math. 1 (1948), 18-28.
11. A. Hubert, R. Schäffer, Magnetic Domains, Springer, Berlin, 1998.
12. R.D. James, D. Kinderlehrer, Frustration in ferromagnetic materials, Continuum Mech. Thermodyn. 2 (1990), 215-239.
13. D. Jiles, A self consistent generalized model for the calculation of minor loop excursions in the theory of hysteresis. IEEE Trans. Mag. 28 (1992), 2603.
14. M. Kružk, Maximum principle based algorithm for hysteresis in micromagnetics. Adv. Math. Sci. Appl. 13 (2003), 461-485.
15. M. Kružk, A. Prohl, Young measure approximation in micromagnetics, Num. Math. 90 (2001), 291-307.
16. M. Kruž, T. Roubček, Weierstrass-type maximum principle for microstructure in micromagnetics, Zeitschrift f. Analysis u. ihre Anwendungen 19 (2000), 415-428.
17. M. Kružk, T. Roubček, Specimen shape influence on hysteretic response of bulk ferromagnets. J. Magnetism & Magn. Mater. 256 (2003), 158-167.
18. L.D. Landau, E.M. Lifshitz, On the theory of the dispersion of magnetic permeability of ferromagnetic bodies. Physik Z. Sowjetunion 8 (1935), 153-169.
19. L.D. Landau. E.M. Lifshitz, Course of Theoretical Physics 8. Pergamon Press, Oxford, 1960.
20. M. Luskin, L. Ma, Analysis of the finite element approximation of microstructure in micromagnetics. SIAM J. Num. Anal. 29 (1992), 320-331.
21. L. Ma, Analysis and computation for a variational problem in micromagnetics, Ph.D. Thesis, University of Minnesota, Minneapolis, 1991.
22. A. Mainik, A. Mielke, Existence results for energetic models for rate-independent materials. Calc. Var. (to appear).
23. A. Mielke, Relaxation via Young measures of material models for rate-independent inelasticity. Preprint SPP 1095 no. 35/2002, Stuttgart, 2002.
24. A. Mielke, Energetic formulation of multiplicative elastoplasticity using dissipation distances. Continuum Mech. Thermodyn. 15 (2003), 351-382.
25. A. Mielke, Analysis of energetic models for rate-independent materials. In: Int. Congress of Math. 2002, Beijing, Vol.III, pp.817-828.
26. A. Mielke, F. Theil, Mathematical model for rate-independent phase transformations. In: Models of Cont. Mechanics in Analysis and Engineering Shaker-Verlag, Aachen, 1999, pp. 117-129.
27. A. Mielke, F. Theil, On rate-independent hysteresis models. Nonlin. Diff. Eq. Appl. 11 (2004), 151-189.
28. A. Mielke, F. Theil, V. Levitas, A variational formulation of rate-independent phase transformations using extremum principle. Arch. Rat. Mech. Anal. 162 (2002), 137-177.
29. P. Pedregal, Relaxation in ferromagnetism: the rigid case. J. Nonlin. Sci. 4 (1994), 105-125.
30. P. Pedregal, Parametrized Measures and Variational Principles, Birkhäuser, Basel, 1997.
31. V. Raposo, J.M. Garcia, J.M. Gonzáles, M. Vázquez, Long-range magnetostatic interactions in arrays of nanowires. J. Magnetism & Magn. Mater. 222 (2000), 227-232.
32. X. Ren, L. Truskinovsky, Finite scale microstructures in nonlocal elasticity. J. Elasticity 59 (2000), 319-355.
33. R.C. Rogers, A nonlocal model for the exchange energy in ferromagnetic materials, J. Int. Eq. Appl. 3 (1991), 85-127.
34. R. Rogers, L. Truskinovsky, Discretization and hysteresis. Physica B 233 (1997), 370-375.
35. T. Roubček, Stable extension of constrained optimization problems. J. Math. Anal. Appl. 141 (1989), 120-135.
36. T. Roubček, Relaxation in Optimization Theory and Variational Calculus, W. de Gruyter, Berlin, 1997.
37. T. Roubček, M. Kružk, Microstructure evolution model in micromagnetics. Zeitschrift f. Angew. Math. Phys. 55 (2004), 159-182.
38. J. Souček, Spaces of functions on domain Ω, whose k-th derivatives are measures defined on Ω. Čas. pro Pěst. Mat. 97 (1972), 10-46.
39. F. Theil, Relaxation of rate-independent evolution problems. Proc. Royal Soc. Edinburgh A 132 (2002), 463-481.
40. A. Visintin, Modified Landau-Lifshitz equation for ferromagnetism, Physica B 233 (1997), 365-369.
41. A. Visintin, On some models of ferromagnetism. In: Free Boundary Problems I Chiba, 1999. (N.Kenmochi, ed.) Gakuto Int. Series in Math. Sci. Appl. 13, 2000, pp.411-428.
42. A. Visintin, A Weiss-type model of ferromagnetism, Physica B 275 (2000), 87-91.
43. L.C. Young, Generalized curves and existence of an attained absolute minimum in the calculus of variations, Comptes Rendus de la Socit et des Lettres de Varsovie, Classe III 30 (1937), 212-234.