August  2015, 8(4): 649-691. doi: 10.3934/dcdss.2015.8.649

Rate-independent memory in magneto-elastic materials

1. 

Università degli Studi del Sannio, P.zza Roma, 21 - 82100, Benevento, Italy, Italy

Received  February 2014 Revised  July 2014 Published  October 2014

These notes origin from a group of lectures given at the Spring School on ``Rate-independent evolutions and hysteresis modelling'' (Hystry 2013), held at Politecnico di Milano and at Università degli Studi di Milano, from May 27 until May 31, 2013. They are addressed to Graduate students in mathematics and applied science, interested in modeling rate-independent effects in smart systems. Therefore, they aim to provide the basic issues concerning modeling of multi-functional materials showing memory phenomena, with emphasis to magnetostrictives, in view of their application to the design of smart devices. Such tutorial summarizes several years activity on these issues that involved the cooperation with several colleagues, among all Dr. P. Krejčí, with whom the authors are indebted.
Citation: Daniele Davino, Ciro Visone. Rate-independent memory in magneto-elastic materials. Discrete & Continuous Dynamical Systems - S, 2015, 8 (4) : 649-691. doi: 10.3934/dcdss.2015.8.649
References:
[1]

J. Atulasimha and A. B. Flatau, A review of magnetostrictive iron-gallium alloys,, Smart Materials and Structures, 20 (2011).  doi: 10.1088/0964-1726/20/4/043001.  Google Scholar

[2]

G. Bertotti, Hysteresis in Magnetism,, Academic Press, (1998).   Google Scholar

[3]

G. Bertotti and I. D. Mayergoyz, eds., The Science of Hysteresis,, Elsevier, (2006).   Google Scholar

[4]

M. Brokate, Some mathematical properties of the preisach model of hysteresis,, IEEE Transactions on Magnetics, 25 (1989), 2922.  doi: 10.1109/20.34325.  Google Scholar

[5]

M. Brokate and J. Sprekels, Hysteresis and PhaseTransitions,, Appl. Math. Sci., (1996).  doi: 10.1007/978-1-4612-4048-8.  Google Scholar

[6]

J. Curie and P. Curie, Développement, par pression de l'ectricité polaire dans les cristaux hémièdres à faces inclinées,, Comptes rend., 91 (1880), 294.   Google Scholar

[7]

J. Curie and P. Curie, Contractions et dilatations produites par des tensions dans les cristaux hémièdres faces faces inclinées,, Comptes rend., 93 (1881), 1137.   Google Scholar

[8]

D. Davino, C. Natale, S. Pirozzi and C. Visone, A fast compensation algorithm for real-time control of magnetostrictive actuators,, J. of Magnetism and Mag. Mat.(JMMM), 290-291 (2005), 290.  doi: 10.1016/j.jmmm.2004.11.435.  Google Scholar

[9]

D. Davino, A. Giustiniani and C. Visone, A two-port nonlinear model for magnetoelastic energy-harvesting devices,, IEEE Transactions on Industrial Electronics, 58 (2001), 2556.  doi: 10.1109/TIE.2010.2062477.  Google Scholar

[10]

D. Davino, A. Giustiniani and C. Visone, Modeling, compensation and control of smart devices with hysteresis,, in Smart Actuation and Sensing Systems - Recent Advances and Future Challenges (ed. Giovanni Berselli), (2012).  doi: 10.5772/51388.  Google Scholar

[11]

G. Engdahl (editor), Handbook of Giant Magnetostrictive Materials,, Academic Press, (2000).   Google Scholar

[12]

P. Ge and M. Jouaneh, Tracking control of a piezoceramic actuator,, IEEE Transactions on Control Syst. Tech., 4 (1996), 209.   Google Scholar

[13]

J. P. Joule, On the effects of magnetism upon the dimensions of iron and steel bars,, Philosophical Magazine Series 3, 30 (1847), 76.  doi: 10.1080/14786444708645656.  Google Scholar

[14]

M. A. Krasnosel'skii and A. V. Pokrovskii, Systems with Hysteresis,, Translated from the Russian by Marek Niezgódka, (1989).  doi: 10.1007/978-3-642-61302-9.  Google Scholar

[15]

P. Krejčí, Hysteresis, Convexity and Dissipation in Hyperbolic Equations,, Gakuto Int. Ser. Math. Sci. Appl., (1996).   Google Scholar

[16]

P. Krejčí, Hysteresis and periodic solutions of semilinear and quasilinear wave equations,, Math. Zeit., 193 (1986), 247.  doi: 10.1007/BF01174335.  Google Scholar

[17]

P. Krejčí, On Maxwell equations with the Preisach hysteresis operator: The one-dimensional time-periodic case,, Apl. Mat., 34 (1989), 364.   Google Scholar

[18]

E. Madelung, Über Magnetisierung durch schnell ver- laufende Ströme und die Wirkungs- weise des Rutherford-Marconischen Magnetdetektors,, Ann. Phys., 17 (1905), 861.   Google Scholar

[19]

I. D. Mayergoyz, Mathematical Models of Hysteresis,, Springer, (1991).  doi: 10.2172/6911694.  Google Scholar

[20]

P. Nordblad, Magnetocaloric materials: Strained relations,, Nature Materials, 12 (2013), 11.  doi: 10.1038/nmat3516.  Google Scholar

[21]

F. Preisach, Über die magnetische Nachwirkung,, Zeit. für Physik., 94 (1935), 277.   Google Scholar

[22]

J. B. Restorff, M. Wun-Fogle, A. E. Clark and K. B. Hathaway, Induced magnetic anisotropy in stress-annealed galfenol alloys,, IEEE Transactions on Magnetics, 42 (2006), 3087.  doi: 10.1109/TMAG.2006.878395.  Google Scholar

[23]

J. Schäfer and H. Janocha, Compensation of hysteresis in solid-state actuators,, Sensors and Actuators A, 49 (1995), 97.   Google Scholar

[24]

A. Visintin, Differential Models of Hysteresis,, Applied Mathematical Sciences, (1994).  doi: 10.1007/978-3-662-11557-2.  Google Scholar

[25]

P. Weiss and J. de Freundereich, Etude de l'aimantation initiale en function de la température,, Arch. Sci. Phys. Nat., 42 (1916).   Google Scholar

[26]

S. Wu and C. Wayman, Martensitic transformations and the shape memory effect in $Ti_{50}$$Ni_{10}$$Au_{40}$ and $Ti_{50}$$Au_{50}$ alloys,, Metallography, 20 (1987), 359.   Google Scholar

show all references

References:
[1]

J. Atulasimha and A. B. Flatau, A review of magnetostrictive iron-gallium alloys,, Smart Materials and Structures, 20 (2011).  doi: 10.1088/0964-1726/20/4/043001.  Google Scholar

[2]

G. Bertotti, Hysteresis in Magnetism,, Academic Press, (1998).   Google Scholar

[3]

G. Bertotti and I. D. Mayergoyz, eds., The Science of Hysteresis,, Elsevier, (2006).   Google Scholar

[4]

M. Brokate, Some mathematical properties of the preisach model of hysteresis,, IEEE Transactions on Magnetics, 25 (1989), 2922.  doi: 10.1109/20.34325.  Google Scholar

[5]

M. Brokate and J. Sprekels, Hysteresis and PhaseTransitions,, Appl. Math. Sci., (1996).  doi: 10.1007/978-1-4612-4048-8.  Google Scholar

[6]

J. Curie and P. Curie, Développement, par pression de l'ectricité polaire dans les cristaux hémièdres à faces inclinées,, Comptes rend., 91 (1880), 294.   Google Scholar

[7]

J. Curie and P. Curie, Contractions et dilatations produites par des tensions dans les cristaux hémièdres faces faces inclinées,, Comptes rend., 93 (1881), 1137.   Google Scholar

[8]

D. Davino, C. Natale, S. Pirozzi and C. Visone, A fast compensation algorithm for real-time control of magnetostrictive actuators,, J. of Magnetism and Mag. Mat.(JMMM), 290-291 (2005), 290.  doi: 10.1016/j.jmmm.2004.11.435.  Google Scholar

[9]

D. Davino, A. Giustiniani and C. Visone, A two-port nonlinear model for magnetoelastic energy-harvesting devices,, IEEE Transactions on Industrial Electronics, 58 (2001), 2556.  doi: 10.1109/TIE.2010.2062477.  Google Scholar

[10]

D. Davino, A. Giustiniani and C. Visone, Modeling, compensation and control of smart devices with hysteresis,, in Smart Actuation and Sensing Systems - Recent Advances and Future Challenges (ed. Giovanni Berselli), (2012).  doi: 10.5772/51388.  Google Scholar

[11]

G. Engdahl (editor), Handbook of Giant Magnetostrictive Materials,, Academic Press, (2000).   Google Scholar

[12]

P. Ge and M. Jouaneh, Tracking control of a piezoceramic actuator,, IEEE Transactions on Control Syst. Tech., 4 (1996), 209.   Google Scholar

[13]

J. P. Joule, On the effects of magnetism upon the dimensions of iron and steel bars,, Philosophical Magazine Series 3, 30 (1847), 76.  doi: 10.1080/14786444708645656.  Google Scholar

[14]

M. A. Krasnosel'skii and A. V. Pokrovskii, Systems with Hysteresis,, Translated from the Russian by Marek Niezgódka, (1989).  doi: 10.1007/978-3-642-61302-9.  Google Scholar

[15]

P. Krejčí, Hysteresis, Convexity and Dissipation in Hyperbolic Equations,, Gakuto Int. Ser. Math. Sci. Appl., (1996).   Google Scholar

[16]

P. Krejčí, Hysteresis and periodic solutions of semilinear and quasilinear wave equations,, Math. Zeit., 193 (1986), 247.  doi: 10.1007/BF01174335.  Google Scholar

[17]

P. Krejčí, On Maxwell equations with the Preisach hysteresis operator: The one-dimensional time-periodic case,, Apl. Mat., 34 (1989), 364.   Google Scholar

[18]

E. Madelung, Über Magnetisierung durch schnell ver- laufende Ströme und die Wirkungs- weise des Rutherford-Marconischen Magnetdetektors,, Ann. Phys., 17 (1905), 861.   Google Scholar

[19]

I. D. Mayergoyz, Mathematical Models of Hysteresis,, Springer, (1991).  doi: 10.2172/6911694.  Google Scholar

[20]

P. Nordblad, Magnetocaloric materials: Strained relations,, Nature Materials, 12 (2013), 11.  doi: 10.1038/nmat3516.  Google Scholar

[21]

F. Preisach, Über die magnetische Nachwirkung,, Zeit. für Physik., 94 (1935), 277.   Google Scholar

[22]

J. B. Restorff, M. Wun-Fogle, A. E. Clark and K. B. Hathaway, Induced magnetic anisotropy in stress-annealed galfenol alloys,, IEEE Transactions on Magnetics, 42 (2006), 3087.  doi: 10.1109/TMAG.2006.878395.  Google Scholar

[23]

J. Schäfer and H. Janocha, Compensation of hysteresis in solid-state actuators,, Sensors and Actuators A, 49 (1995), 97.   Google Scholar

[24]

A. Visintin, Differential Models of Hysteresis,, Applied Mathematical Sciences, (1994).  doi: 10.1007/978-3-662-11557-2.  Google Scholar

[25]

P. Weiss and J. de Freundereich, Etude de l'aimantation initiale en function de la température,, Arch. Sci. Phys. Nat., 42 (1916).   Google Scholar

[26]

S. Wu and C. Wayman, Martensitic transformations and the shape memory effect in $Ti_{50}$$Ni_{10}$$Au_{40}$ and $Ti_{50}$$Au_{50}$ alloys,, Metallography, 20 (1987), 359.   Google Scholar

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