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Modeling of non-ideal hard permanent magnets with an affine-linear model, illustrated for a bar and a horseshoe magnet

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Abstract

This study is dedicated to continuum-scale material modeling of isotropic permanent magnets. An affine-linear extension to the commonly used ideal hard model for permanent magnets is proposed, motivated, and detailed. In order to demonstrate the differences between these models, bar and horseshoe magnets are considered. The structure of the boundary value problem for the magnetic field and related solution techniques are discussed. For the ideal model, closed-form analytical solutions were obtained for both geometries. Magnetic fields of the boundary value problems for both models and differently shaped magnets were computed numerically by using the boundary element method. The results show that the character of the magnetic field is strongly influenced by the model that is used. Furthermore, it can be observed that the shape of an affine-linear magnet influences the near-field significantly. Qualitative comparisons with experiments suggest that both the ideal and the affine-linear models are relevant in practice, depending on the magnetic material employed. Mathematically speaking, the ideal magnetic model is a special case of the affine-linear one. Therefore, in applications where knowledge of the near-field is important, the affine-linear model can yield more accurate results—depending on the magnetic material.

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References

  1. Ahrens, J., Geveci, B., Law, C.: Paraview: an end-user tool for large-data visualization. In: Hansen, C.D., Johnson, C.R. (eds.) Visualization Handbook, chap 36, pp. 717–731. Butterworth-Heinemann, Burlington (2005). doi:10.1016/B978-012387582-2/50038-1

    Chapter  Google Scholar 

  2. Alnæs, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M., Wells, G.: The fenics project version 1.5. Arch Numer Softw 3(100), 9–23 (2015). doi:10.11588/ans.2015.100.20553

    Google Scholar 

  3. Andjelic, Z., Of, G., Steinbach, O., Urthaler, P.: Boundary element methods for magnetostatic field problems: a critical view. Comput Vis Sci 14(3), 117–130 (2011). doi:10.1007/s00791-011-0167-3

    Article  MathSciNet  MATH  Google Scholar 

  4. Arfken, G.B., Weber, H.J.: Mathematical methods for physicist, 6th edn. Elsevier Academic Press, Amsterdam (2005)

    MATH  Google Scholar 

  5. Austin, F.E.: Examples in Magnetism, 2nd edn. Hanover (1916)

  6. Becker, R.: Electromagnetic fields and interactions. Dover Publications, Mineola (2013)

    Google Scholar 

  7. Black, N.H., Davis, H.N.: Practical physics. Macmillan, New York (1913)

    Google Scholar 

  8. Bronstein, I.N., Semendjajew, K.A., Musiol, G., Mühlig, H.: Taschenbuch der Mathematik, 9th edn. Edition Harri Deutsch. Verlag Europa Lehrmittel, Haan-Gruiten (2013)

    MATH  Google Scholar 

  9. Burg, K., Haf, H., Wille, F., Meister, A.: Partielle Differentialgleichungen und funktionalanalytische Grundlagen, 5th edn. Vieweg + Teubner, Wiesbaden (2010)

    Book  Google Scholar 

  10. Chen, G., Zhou, J.: Boundary element methods. Computational mathematics and applications. Academic Press, London (1992)

    Google Scholar 

  11. Coey, J.M.D.: Magnetism and magnetic materials. Cambridge University Press, Cambridge (2009)

    Google Scholar 

  12. Furlani, E.P.: Permanent magnet and electromechanical devices. Academic Press Series in Electromagnetism. Academic Press, San Diego (2001). doi:10.1016/B978-012269951-1/50005-X

    Google Scholar 

  13. Guhlke, C.: Theorie der elektrochemischen Grenzfläche. Ph.D. thesis, Technische Universität Berlin (2015)

  14. Jackson, J.D.: Classical electrodynamics, 2nd edn. Wiley, New York (1975)

    MATH  Google Scholar 

  15. Jiles, D.: Introduction to magnetism and magnetic materials, 3rd edn. CRC Press, Boca Raton (2015)

    Google Scholar 

  16. Kovetz, A.: Electromagnetic theory. Oxford University Press, Oxford (2000)

    MATH  Google Scholar 

  17. Mladenovic, A.N., Aleksic, S.R.: Determination of magnetic field for different shaped permanent magnets. In: 7th international symposium on electromagnetic compatibility and electromagnetic ecology, pp. 84–87. IEEE (2007). doi:10.1109/EMCECO.2007.4371653

  18. Müller, W.H.: An expedition to continuum theory. Solid mechanics and its applications. Springer, New York (2014)

    Book  Google Scholar 

  19. Patsyk, A.: Computational physics project (2016). http://phelafel.technion.ac.il/~anatoly/magnetic_results.html

  20. Rjasanow, S., Steinbach, O.: The fast solution of boundary integral equations. Mathematical and analytical techniques with applications to engineering. Springer, Berlin (2007)

    MATH  Google Scholar 

  21. Sauter, S.A., Schwab, C.: Boundary element methods. Springer Series in Computational Mathematics, vol. 39. Springer, Berlin (2011)

    Book  Google Scholar 

  22. Śmigaj, W., Betcke, T., Arridge, S., Phillips, J., Schweiger, M.: Solving boundary integral problems with bem++. ACM Trans. Math. Softw. 41(2), 6:1–6:40 (2015). doi:10.1145/2590830

    MathSciNet  MATH  Google Scholar 

  23. Truesdell, C.A., Toupin, R.: The classical field theories. In: Handbuch der Physik, Bd. III/1, pp. 226–793; appendix, pp. 794–858. Springer, Berlin (1960). With an appendix on tensor fields by J. L. Ericksen

  24. Wolfram Research, Inc.: Mathematica. Champaign, Illinois (2015). Version 10.1

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Authors and Affiliations

  1. Institut für Mechanik, Kontinuumsmechanik und Materialtheorie, Technische Universität Berlin, Sek. MS. 2, Einsteinufer 5, 10587, Berlin, Germany

    Sebastian Glane, Felix A. Reich & Wolfgang H. Müller

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  1. Sebastian Glane
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  2. Felix A. Reich
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  3. Wolfgang H. Müller
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Correspondence to Sebastian Glane.

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Communicated by Andreas Öchsner.

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Glane, S., Reich, F.A. & Müller, W.H. Modeling of non-ideal hard permanent magnets with an affine-linear model, illustrated for a bar and a horseshoe magnet. Continuum Mech. Thermodyn. 29, 1313–1333 (2017). https://doi.org/10.1007/s00161-017-0578-6

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  • DOI: https://doi.org/10.1007/s00161-017-0578-6

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