Skip to main content
SpringerLink
Log in

Non-Equilibrium Thermodynamics of Electromagnetic Solids

  • Chapter
Non-Equilibrium Thermodynamics with Application to Solids

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 336))

Abstract

The thermomechanics of electromagnetic continua is a branch of energetics which deals with a unification of continuum mechanics and electrodynamics of material media under the umbrella of general thermodynamics. This obviously goes in the direction indicated by the great P.Duhem early in this century (Duhem, 1911, 1914/1954). This ambitious, somewhat Aristotelian-like, scheme also adds one difficulty to the other. In effect, in addition to the cumbersome and rather heavy framework of nonlinear continuum mechanics (such as exposed in modern treatises, e.g., Truesdell and Toupin, I960, Truesdell and Noll, 1965; Eringen 1980, Eringen 1971–1976), one has to consider electromagnet ism (e.g., Jackson, 1962) and then combine them (in an nonlinear manner; this is not a linear superposition) in the harmonious frame of thermodynamics. Some of the difficulties met have to do with the electrodynamics of moving bodies (writing of fields and equations in appropriate frames), while others relate to the introduction of a general deformation field (“material” writing of fields). Finally, there are difficulties connected with the inherent complexity of some of the behaviors (e.g., hysteresis), and even more so, the non-unique thermodynamical framework at the time of writing!

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • BAMPI. and MORRO A., (1981), Dissipative Effects and waves in Magnetofluidynamics, J. Non-Ecruilib.Thermodynam., 6, 1–14.

    Article  MATH  MathSciNet  Google Scholar 

  • BASSIOUNY E., GHALEB A.F. and MAUGIN G.A., (1988a), Thermodynamical Formulation for Coupled Electromechanical Hysteresis-I-Basic Equations, Int.J.Engng.Sci., 26, 1279–1295.

    Article  MATH  MathSciNet  Google Scholar 

  • BASSIOUNY E., GHALEB A.F. and MAUGIN G.A., (1988b), Thermodynamical Formulation for Coupled Electromechanical Hysteresis — II — Poling of Ceramics, Int. J. Engng. Sci., 26, 1297–1306.

    Article  MATH  MathSciNet  Google Scholar 

  • BASSIOUNY E. and MAUGIN G.A., (1989a), Thermodynamical Formulation for Coupled Electromechanical Hysteresis — III — Parameter Identification, Int.J.Engng.Sci., 27, 975–987.

    Article  MATH  MathSciNet  Google Scholar 

  • BASSIOUNY E. and MAUGIN G.A., (1989b), Thermodynamical Formulation for Coupled Electromechanical Hysteresis IV Combined Electromechanical Loadings, Int.J.Engng.Sci., 27, 989–1000.

    Article  MATH  MathSciNet  Google Scholar 

  • BATAILLE J. and KESTIN J., (1975), L’interprétation physique de la thermodynamique rationnelle, J.Mécanique, 14, 365–384.

    MATH  MathSciNet  Google Scholar 

  • BRIDGMAN P.W., (1941), The Nature of Thermodynamics, Harvard University Press, Cambridge, Mass. (New Edition, Harper and Brothers, New York, 1961).

    Google Scholar 

  • CHEN P.J., (1980), Three-dimensional Dynamic Electromechanical Constitutive Relations for Ferroelectric Materials, Int.J.Solids Struct., 16, 1059–1067.

    Article  MATH  Google Scholar 

  • CHEN P.J., (1984), Hysteresis Effects in Deformable Ceramics, in: The Mechanical Behavior of Electromagnetic Solid Materials, ed. G.A. Maugin, pp.137–143, North-Holland, Amsterdam.

    Google Scholar 

  • CHEN P.J. and PEERCY P.S., (1979), One-dimensional Dynamic Electromechanical Constitutive Equations of ferroelectric Materials, Acta Mechanica, 31, 231–241.

    Article  MATH  MathSciNet  Google Scholar 

  • CHERNYI L.T., (1983), Models of Ferromagnetic Continua with Magnetic Hysteresis, in: Macroscopic Theories of Matter and Fields, ed. L.I. Sedov, pp.116–140, Mir Publishers, Moscow.

    Google Scholar 

  • CHUA L.O. and STROMSMOE K.A., (1971), Mathematical Models for Dynamic Hysteresis Loops, Int. J.Engng. Sci., 9, 564–574.

    Google Scholar 

  • COLLET B., (1983), Shock Waves in Deformable Piezoelectric Materials, in: Proc. llth Intern. Congress of Acoustics, Special Issue of Revue d’Acoustique, Vol.2, Sec.2.1, pp.125–128.

    Google Scholar 

  • COLLET B., (1984), Shock Waves in Deformable Ferroelectric Materials, in: The Mechanical Behavior of Electromagnetic Solid Materials, ed. G.A. Maugin, pp.157–163, North-Holland, Amsterdam.

    Google Scholar 

  • COLLET B., (1985), Nonlinear Wave propagation in Elastic Dielectrics with Internal Variables, J.Techn. Physics, 26, 285–289.

    Google Scholar 

  • COLLET B., (1987), Transient Nonlinear Waves in Elastic Dielectric Materials, in: Electromagnetomechanical Interactions in Deformable Solids and Structures, eds. Y. Yamamoto and K. Miya, pp.329–334, North-Holland, Amsterdam.

    Google Scholar 

  • DAHER N. and MAUGIN G.A., (1987), Deformable Semiconductors with Interfaces: Basic Equations, Int.J.Engng.Sci., 25, 1093–1129.

    Article  MATH  MathSciNet  Google Scholar 

  • DE GENNES P.G.(1966/1989), Superconductivity of Metals and Alloys, W.A.Benjamin, New York (New Edition, 1989).

    Google Scholar 

  • DE GROOT S.R. and SUTTORP L.G., (1972), Foundations of Electrodynamics, North-Holland, Amsterdam.

    Google Scholar 

  • DROUOT R. and MAUGIN G.A., (1985), Continuum Modelling of Polyelectrolytes in Solution, Rheologica Acta, 24, 474–487.

    Article  MATH  Google Scholar 

  • DUHEM P. (1911), Traité d’Energétique ou de Thermodynamique Générale, Two volumes, Gauthier-Villars, Paris.

    MATH  Google Scholar 

  • DUHEM P., (1914/1954), The Aim and Structure of Physical Theory, Princeton University Press, Princeton, N.J. (1954; Translation from the Second French Edition, Rivière, Paris, 1914).

    MATH  Google Scholar 

  • ERINGEN A.C. (1971–1976;Editor), Continuum Physics, Four volumes, Academic Press, new York.

    Google Scholar 

  • ERINGEN A.C., (1980), Mechanics of Continua, Revised and enlarged Edition, Krieger, new York.

    Google Scholar 

  • ERINGEN A.C. and MAUGIN G.A., (1990), Electrodynamics of Continua, Two volumes, Springer-Verlag, New York.

    Google Scholar 

  • FOMETHE A. and MAUGIN G.A., (1982), Influence of Dislocations on Magnon-Phonon Couplings. A Phenomenological Approach, Int.J.Engng.Sci., 20, 1125–1144.

    Article  MATH  MathSciNet  Google Scholar 

  • GERMAIN P., NGUYEN QUOC SON and SUQUET P., (1983), Continuum Thermodynamics, ASME Trans.J.Appl.Mech., 105, 1010–1020.

    Article  Google Scholar 

  • JACKSON J.D. (1962), Classical Electrodynamics, J.Wiley, New York.

    Google Scholar 

  • JOU D., CASAS-VASQUEZ J. and LEBON G., (1988), Extended Irreversible Thermodynamics Review, Rep.Prog, in Physics, 9, 1105–1179.

    Article  Google Scholar 

  • KARJALAINEN L.P. and MOILAMEN M., (1979), Detection of Plastic Deformation during Fatigue of Mild Steel by the Measurement of the Barkhausen Noise, NDT International, No.4, 51–55.

    Google Scholar 

  • KLUITENBERG G.A., (1973), On Dielectric and Magnetic Relaxation Phenomena and Non-equilibrium Thermodynamics, Physica, 68, 75–92.

    Article  Google Scholar 

  • KLUITENBERG G.A., (1977), On Dielectric and Magnetic Relaxation Phenomena and Vectorial Integranl Degrees of Freedom in Thermodynamics, Physica, 87A, 302–330.

    Article  Google Scholar 

  • KLUITENBERG G.A., (1981a), On Vectorial Internal Variables and Dielectric and Magnetic Relaxation Phenomena, Physica, 109A, 91–122.

    Article  MathSciNet  Google Scholar 

  • KLUITENBERG G.A., (1981b), On Transformations of Internal Variables in the Thermodynamic Theory of a..., Physica, 109A, 123–127.

    Article  MathSciNet  Google Scholar 

  • LOBANOV E.N., (1991), Theory of Superconducting Composites, Mekh. Komposit Materialov (in Russian), in the press.

    Google Scholar 

  • LYNTON E.A., (1969), Superconductivity, Methuen and Co. (3rd Edition)- New Printing: Science Paperback, Chapman and Hall, London (1971).

    Google Scholar 

  • MAUGIN G.A., (1979a), Internal Variables in Ferroelectric and Ferromagnetic Continua, in: Recent Developments in the Theory and Application of Generalized and Oriented Media, pp.201–204, American Academy of Mechanics, Calgary, Canada.

    Google Scholar 

  • MAUGIN G.A., (1979b), Vectorial Internal Variables in Magnetoelasticity, J.Mécanique, 18, 541–563.

    MATH  MathSciNet  Google Scholar 

  • MAUGIN G.A., (1980), The Method of Virtual Power in Continuum Mechanics: Application to Coupled Fields, Acta Mechanica, 35, 1–70.

    Article  MATH  MathSciNet  Google Scholar 

  • MAUGIN G.A., (1981a), Electromagnetic Internal variables in Electromagnetic Continua, Arch. Mech., 33, 927–935.

    MATH  MathSciNet  Google Scholar 

  • MAUGIN G.A., (1981b), Simple Thermodynamical Model for Rigid Ferromagnets, Phys. Rev., B25, 7019–7025.

    Article  Google Scholar 

  • MAUGIN G.A., (1985), Nonlinear Electromechanical Effects and Applications (A Series of Lectures), World Scientific, Singapore.

    Google Scholar 

  • MAUGIN G.A., (1988), Continuum Mechanics of Electromagnetic Solids, North-Holland, Amsterdam (in Russian translation, MIR, Moskva, 1991).

    MATH  Google Scholar 

  • MAUGIN G.A., (1989), Coupled Magnetomechanical and Electromechanical Hysteresis Effects, in: Applied Electromagnetics in Materials, eds. R.K.T. Hsieh and K. Miya, pp.5–18, Pergamon Press, London, Tokyo.

    Google Scholar 

  • MAUGIN G.A., (1990), Internal Variables and Dissipative Structures, J. Non-Equilibr. Thermodyn., 15, 173–192.

    Google Scholar 

  • MAUGIN G.A., (1991a), Thermodynamics of Hysteresis, in: Non-equilibrium Thermodynamics, Vol.7, “Extended Thermodynamics”, pp.25–52, eds. D. Salamon and S. Sieniutycz, Taylor and Francis, New York.

    Google Scholar 

  • MAUGIN G.A., (1991b), Compatibility of Magnetic Hysteresis with Thermodynamics, Int.J.Appl.Electrom.Mat., 2, 7–19.

    Google Scholar 

  • MAUGIN G.A., (1991c), The Thermomechanics of Plasticity and Fracture, Cambridge University Press (in Russian translation, MIR, Moskva, 1993).

    Google Scholar 

  • MAUGIN G.A., (1992a), Irreversible Thermodynamics of Elastic Superconductors, C.R.Acad.Sci.Paris, 11–314.

    Google Scholar 

  • MAUGIN G.A., (1992b), Material Inhomogeneities in Elasticity, Chapman and Hall, London.

    Google Scholar 

  • MAUGIN G.A., COLLET B., and POUGET J., (1986), Nonlinear Wave Propagation in Coupled Electromechamical Systems,, in: Nonlinear Wave propagation in Solids, ed. T.W. Wright, ASME Publ.Vol.AMD-77, pp.57–84, ASME, New York.

    Google Scholar 

  • MAUGIN G.A., COLLET B., DROUOT R. and POUGET J., (1992), Nonlinear Electromechanical Couplings, Manchester University Press, Manchester, U.K.

    Google Scholar 

  • MAUGIN G.A. and BASSIOUNY E., (1989), Continuum Thermodynamics of Electromechanical Hysteresis in Ceramics, in: Continuum Mechanics and its Applications, eds. G.A. C. Graham et al, pp. 225–235, Hemisphere Publ., New York.

    Google Scholar 

  • MAUGIN G.A. and DAHER N., (1986), Phenomenological Theory of Elastic Piezoelectric Semiconductors, Int.J. Engng. Sci., 21, 703–731.

    Article  MathSciNet  Google Scholar 

  • MAUGIN G.A. and DROUOT R., (1983), Thermomagnetic Behavior of Magnetically Non-saturated Fluids, J. Magnetism and Magnetic Materials, 39, 7–10.

    Article  Google Scholar 

  • MAUGIN G.A. and ERINGEN A.C., (1977), On the Equations of the Electrodynamics of Deformable Solids of Finite Extent, J.Mécanique, 16, 101–147.

    MATH  MathSciNet  Google Scholar 

  • MAUGIN G.A. and FOMETHE A., (1982), On the Elastoviscoplasticity of Ferromagnetic Crystals, Int. J. Engng. Sci., 20, 885–908.

    Article  MATH  MathSciNet  Google Scholar 

  • MAUGIN G.A. AMD MILED A., (1986), Solitary Waves in Elastic Ferromagnets, Phys. Rev., B33, 4830–4832.

    Article  Google Scholar 

  • MAUGIN G.A. and MUSCHIK W., (1992), Thermodynamics with Internal variables: A Review, I-Generalities, II-Applications, J. Non-Equilibr. Thermodyn.

    Google Scholar 

  • MAUGIN G.A. and POUGET J., (1980), Electroacoustic Equations for One-domain Ferroelectric Bodies, J. Acoust. Soc.Amer., 68, 575–587.

    Article  MATH  Google Scholar 

  • MAUGIN G.A. and SABIR M., (1990), Mechanical and Magnetic Hardening of Ferromagnetic Bodies: Influence OF residual Stresses and Application to Nondestructive Testing, Int. J.of Plasticity, 6, 573–589.

    Article  MATH  Google Scholar 

  • MAUGIN G.A., SABIR M. and CHAMBON P., (1987), Coupled Magnetomechanical Hysteresis in Ferromagnets: Application to Nondestructive Testing, in: Electromagnetomechanical Interactions in Deformable Solids and Structures, eds.Y. Yamamoto and K. Miya, pp.255–264, North-Holland, Amsterdam.

    Google Scholar 

  • MCCARTHY M.F., (1984a), One-Dimensional Shock Waves in Deformable Dielectrics with Internal State Variables, Arch.Mech., 35, 97–107.

    Google Scholar 

  • MCCARTHY M.F., (1984b), One-Dimenisonal Pulse Propagation in Deformable Dielectrics with Internal State Variables, Arch.Rat.Mech.Anal., 86, 353–367.

    Article  MATH  Google Scholar 

  • MEIXNER J., (1961), Der Drehimpulssatz in der Thermodynamik der irreversible Prozessen, Zeit.Phys., 16, 145–155.

    Article  MathSciNet  Google Scholar 

  • MORRO A., DROUOT R. and MAUGIN G.A., (1985), Thermodynamics of Polyelectrolyte Solutions in an Electric Field, J.Non-Equilibr. Thermodyn., 10, 131–144.

    Google Scholar 

  • MORRO A., MAUGIN G.A. and DROUOT R., (1990), Diffusion in Polyelectrolyte Solutions, Rheologica Acta, 29, 215–222.

    Article  Google Scholar 

  • MULLER I., (1985), Thermodynamics, Pitman (now Longman), London.

    Google Scholar 

  • MUSCHIK W., (1990a), Internal Variables in Non-equilibrium Thermodynamics, J.Non-equilibr.Thermodyn., 15, 127–137.

    Google Scholar 

  • MUSCHIK W., (1990b), Aspects of Non-equilibrium Thermodynamics: Six Lectures on Fundamentals and Methods, World Scientific, Singapore.

    Google Scholar 

  • NEEL L., (1946), Bases d’une nouvelle théorie générale du champ coercitif, Ann. Univ. Grenoble, 22, 299–343.

    MathSciNet  Google Scholar 

  • NELSON D.F., (1979), Electric, Optic and Acoustic Interactions in Dielectrics, J.Wiley-Interscience, New York.

    Google Scholar 

  • PARKUS H., (1979;Editor), Electromagnetic Interactions in Elastic Solids (CISM Lecture Notes, 1977), Springer-verlag, Wien.

    Google Scholar 

  • PARRY G.P., (1987), On Internal Variable Models of Phase Transitions, J. of Elasticity, 17, 63–70.

    Article  MATH  MathSciNet  Google Scholar 

  • POUGET J. and MAUGIN G.A., (1984), Solitons and Electroacoustic Interactions in ferroelectric Crystals-I, Phys. Rev., B30, 5306–5325.

    Article  Google Scholar 

  • PRAGER W., (1957), On Ideal Locking Materials, Trans.Soc.Rheology, 1, 169–175.

    Article  MATH  Google Scholar 

  • PREISACH F., (1935), Uber die magnetische Nachwirkung, Zeit. Phys., 94, 277–302.

    Article  Google Scholar 

  • ROSENSWEIG R.E., (1989), Thermodynamics of Electromagnet ism, in: Thermodynamics: An Advanced Textbook for Chemical Engineers, by G. Astarita, Plenum, New York.

    Google Scholar 

  • RUDYAK V.M., (1971), The Barkhausen Effects, Sov.Phys. Uspekhi, 13, 451–479.

    Google Scholar 

  • SABIR M. and MAUGIN G.A., (1988), Microscopic Foundations of the barkhausen Effect, Arch. Mech., 40, 829–841.

    MATH  MathSciNet  Google Scholar 

  • TIERSTEN H.F., (1990), A Development of the Equations of Electromagnetism in Material Continua, Springer-verlag, New York.

    Book  MATH  Google Scholar 

  • TINKHAM M., (1964), Phys. Rev. Lett., 13, 804.

    Article  Google Scholar 

  • TRUESDELL C.A. and NOLL W., (1965), Nonlinear Field Theories of Mechanics, in:Handbuch der Physik, Bd.II1/3, ed. S. Flügge, Springer-verlag, Berlin.

    Google Scholar 

  • TRUESDELL C.A. and TOUPIN R.A., (1960), The Classical Field Theories, in: Handbuch der Physik, Bd.III/1, ed. S. Flügge, Springer-verlag, Berlin.

    Google Scholar 

  • YAKUSHCOV V.V., ROZANOV D.K. and DREMIN A.N., (1968), On the Measurement of the Polarization relaxation Time in a Shock wave, Sov. Phys. JETP, 27, 213–215.

    Google Scholar 

  • ZHOU S.A. and MIYA K., (1991), A Nonequilibrium Theory of Thermoelastic Superconductors, Int. J. Appl. Electromag. Mat., 2, 21–38.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. C.N.R.S., Université Pierre-et-Marie Curie, Paris, France

    G. A. Maugin

  2. Institute for Advanced Study Berlin, Berlin, Germany

    G. A. Maugin

Authors
  1. G. A. Maugin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Technical University, Berlin, Germany

    W. Muschik

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Wien

About this chapter

Cite this chapter

Maugin, G.A. (1993). Non-Equilibrium Thermodynamics of Electromagnetic Solids. In: Muschik, W. (eds) Non-Equilibrium Thermodynamics with Application to Solids. International Centre for Mechanical Sciences, vol 336. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4321-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-4321-6_4

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82453-5

  • Online ISBN: 978-3-7091-4321-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation