Skip to main content

Material Mechanics of Electromagnetic Solids

  • Chapter
Configurational Mechanics of Materials

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 427))

Abstract

Eshelby [1–5] introduced the notion (and the naming) of Maxwell stress tensor of Elasticity having in mind the Maxwell energy-stress of electromagnetism.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

  1. Eshelby J.D., (1951), Force on an Elastic Singularity, Phil. Tran. Roy. Soc. Lond., A244, 87–112.

    Article  MathSciNet  MATH  Google Scholar 

  2. Eshelby J.D., (1956), Continuum Theory of lattice Defects, in: Progress in Solid State Physics, Eds. F. Seitz and D.Turnbull, Vol. 3, p. 79, Academic Press, New York.

    Google Scholar 

  3. Eshelby J.D., (1975), Elastic Energy-momentum Tensor, J. of Elasticity, 5, 321–335.

    Article  MathSciNet  MATH  Google Scholar 

  4. Eshelby J.D., (1970), Energy Relations and the Energy-momentum Tensor in Continuum Mechanics, in: Inelastic Behavior of Solids, Eds. M.F. Kanninen, W.F. Adler, A.R. Rosenfeld, and R.I. Jaffe, pp. 77–114, McGraw Hill, New York.

    Google Scholar 

  5. Eshelby J.D., (1982), Aspects of Dislocation Theory, in: Mechanics of Solids (The Rodney Hill 60th Anniversary Volume), eds. H.G. Hopkins and M. Sewell, pp. 185–255, Pergamon Press, Oxford.

    Google Scholar 

  6. Nelson D.F., (1979), Electric, Optic and Acoustic Interactions in Dielectrics, John Wiley, New York.

    Google Scholar 

  7. Nelson D.F., (1991), Momentum, Pseudomomentum and Wave Momentum: Toward Resolving the Minkowski-Abraham Controversy, Phys. Rev., A44, 3905–3916.

    Google Scholar 

  8. Peierls R., (1979), Surprises in Theoretical Physics,Princeton Univ.Press.

    Google Scholar 

  9. Peierls R., (1985), Momentum and Pseudomomentum of Light and Sound, i n: Highlights of Condensed-Matter Physics, Ed. M. Tosi, Corso LXXXIX, pp. 237–255, Soc.Ital. Fisica, Bologna.

    Google Scholar 

  10. Eringen A.C. and Maugin G.A., (1990), Electrodynamics of Continua, Two volumes, Springer-Verlag, New York.

    Google Scholar 

  11. Maugin G.A., (1988), Continuum Mechanics of Electromagnetic Solids, (Vol.33 of Series in Applied Mathematics and Mechanics), North-Holland, Amsterdam.

    Google Scholar 

  12. Eshelby J.D., (1980), The Force on a Disclination in a Liquid Crystal, Phil. Mag., A42, 354–367.

    Google Scholar 

  13. Ericksen J.L., (1995), Remarks concerning Forces on Line Defects, Zeit. Angew. Math. Phys., (Special issue: Theoretical, Experimental and Numerical Contributions to the Mechanics of Fluids and Solids, dedicated to P.M.Naghdi), 46S, 247–2271.

    MathSciNet  Google Scholar 

  14. Kröner E., (1993), Configurational and Material Forces in the Theory of Defects in Ordered Structures, CMDS 7 Proceedings, K.H. Anthony and H.J. Wagner Editors, Material Science Forum, 123–125, 447–454.

    Google Scholar 

  15. Maugin G.A. and Trimarco C., (1995b), On Material and Physical Forces in Liquid Crystals, Int. J. Engng. Sci., 33, 1663–1678.

    Article  MathSciNet  MATH  Google Scholar 

  16. Ogden R.W., (1984), Nonlinear Elastic Deformations, Ellis Horwood, Chichester, U.K (Dover reprint, New York, 1997 ).

    MATH  Google Scholar 

  17. Reissner E., (1953), Variational Theorem for Finite Elastic Deformations, J. Math. and Phys. (MIT), 32, 129–135.

    MathSciNet  MATH  Google Scholar 

  18. Maugin G.A. and Trimarco C., (1993), Note on Mixed Variational Principle in Finite Elasticity, Rend. Mat. Accad. Lincei, IX-III, 69–74.

    Google Scholar 

  19. Knops R., Trimarco C. and Williams H.T., Uniqueness and Complementary Energy in Finite Elasticity. (Forthcoming).

    Google Scholar 

  20. Hanyga A., (1985), Mathematical Theory of Nonlinear Elasticity, Ellis Horwood„Chichester, U.K.

    MATH  Google Scholar 

  21. Golebiewska-Herrmann A, (1983), Lagrangian Formulation of Continuum Mechanics, Physica, 118A, 300–314.

    Article  MathSciNet  MATH  Google Scholar 

  22. Pack Y.E. and Herrmann G., (1986a), Conservation Laws and the Material Momentum Tensor for the Elastic Dielectric, Int. J. Engng. Sci., 24, 1365–1374.

    Article  Google Scholar 

  23. Maxwell J. C., (1891), A Treatise on Electricity and Magnetism,volumes I and II, Oxford Classic Text in the physical Sciences, Clarendon Press, Oxford,,(1998, reprint)

    Google Scholar 

  24. Becker R., Electromagnetic Fields and Interactions,Dover Publ., NewYork, (1982, reprint).

    Google Scholar 

  25. Stratton J. A. (1941), Electromagnetic Theory, McGraw-Hill, New York.

    MATH  Google Scholar 

  26. Jackson J.D., (1962), Classical Electrodynamics,J. Wiley & Sons,N.Y.

    Google Scholar 

  27. Tamm I E, (1979), Fundamentals of the Theory of Electricity, translated from the 1976 Russian edition, MIR Publishers.

    Google Scholar 

  28. Landau L.D. and Lifschitz E.M., (1960), Electrodynamics of Continuous Media, v. 8 of Course of Theoretical Physics, Pergamon Press, Oxford.

    Google Scholar 

  29. Penfield P. and Haus H. A., (1967), Electrodynamics of Moving Media, M. I. T. Press, Cambridge, Massachusetts.

    Google Scholar 

  30. Pao Y. H., (1978), Electromagnetic Forces in Deformable Continua, Mechanics Today, vol 4, S. Nemat-Nasser Editor, Pergamon Press, New York.

    Google Scholar 

  31. Trimarco C.: (1994). How Multipole Electric Moments Enter into Macroscopic Maxwell Equations, Il Nuovo Cimento B, 109, 533–540.

    Google Scholar 

  32. Toupin R.A., (1956), The Elastic Dielectrics, J. Rational Mech and Anal., 5, (849–915).

    Google Scholar 

  33. Schoeller H. and Thellung A., (1992) Lagrangian Formalism and Conservation Law for Electrodynamics in Nonlinear Elastic Dielectrics, Annals of Physics, 220–1.

    Google Scholar 

Additional references for further studies

  • Chadwick P., (1975), Applications of an Energy-momentum Tensor in Nonlinear Elastostatics, J. Elasticity, 5, 250–258.

    MathSciNet  Google Scholar 

  • Cherepanov G.P., (1989), Remark on the Dynamic Invariant or Path-independent Integral, Int.J Solids Structures, 25, 1267–9.

    Article  MATH  Google Scholar 

  • Dascalu C. and Maugin G.A., (1994), Energy-release Rates and Path-independent Integrals in Electroelastic Crack Propagation, Int.J.Engng.Sci., 32, 755–765.

    Article  MathSciNet  MATH  Google Scholar 

  • Edelen D.G.B., (1981), Aspects of Variational Arguments in the Theory of Elasticity: Facts and Folklore, Int. J. Solids Structures, 17, 729–740.

    Article  MathSciNet  MATH  Google Scholar 

  • Ericksen J.L., (1977), Special topics in Elastostatics, in: Advances in Applied Mechanics, Ed. C-S.Yih, Vol. 17, pp. 189–244, Academic Press, New York.

    Google Scholar 

  • Ericksen J.L., (1991), Introduction to the Thermomechanics of Solids, Chapman and Hall, London.

    Google Scholar 

  • Ericksen J.L., (1997), Equilibrium Theory for X-ray Observations of Crystals, Arch. Rat. Mech. Anal., 139, 181–200.

    Article  MathSciNet  MATH  Google Scholar 

  • Fomethe A. and Maugin G.A., (1996), Material Forces in Thermoelastic Ferromagnets Cont. Mech. and Thermodynamics, 8, 275–292.

    Article  MathSciNet  MATH  Google Scholar 

  • Golebiewska-Herrmann A., (1981), On Conservation Laws of Continuum Mechanics, Int. J. Solids Structures, 17, 1–9.

    Article  MathSciNet  Google Scholar 

  • Green A.E., (1973), On Some General Formulae in Finite Elastostatics, Arch.Rat.Mech.Anal., 50, 73–80.

    MATH  Google Scholar 

  • Grinfeld M.A. (1991), Thermodynamic Methods in the Theory of Heterogeneous Systems, ISIMM Series, Longman, Harlow, Essex.

    Google Scholar 

  • Gurtin M.E., (2000), Configurational Forces as Basic Concepts of Continuum Physics, Springer-Verlag, New York.

    Google Scholar 

  • Herrmann G., (1980), Some Applications of Invariant Variational Principles in Mechanics of Solids, in: Variational Methods in the Mechanics of Solids (IUTAM Symp.,Evanston, 1978), pp. 145–150, Pergamon Press, Oxford.

    Google Scholar 

  • Hill R., (1986), Energy-momentum Tensor in Elastostatics: Some reflections on the General Theory, J. Mech. Phys. Solids, 34, 305–317.

    Article  MathSciNet  MATH  Google Scholar 

  • Knowles J.K., and Sternberg E., (1972), Class of Conservation Laws in Linearized and Finite Elastostatics, Arch. Rat. Mech. Anal., 44, 187–211.

    MathSciNet  MATH  Google Scholar 

  • Maugin G.A., (1993), Material Inhomogeneities in Elasticity,Chapman and Hall, London (Volume 3 in Series «Applied Mathematics and Mathematical Computation).

    Google Scholar 

  • Maugin G.A., (1997), Momentum and Pseudomomentum in Matter, GAMM-Mitteilungen, Heft 1, 37–51.

    MathSciNet  Google Scholar 

  • Maugin G.A., (1999), Nonlinear Waves in Elastic Crystals, Oxford Texts in Applied Mathematics, Oxford University Press, U.K.

    MATH  Google Scholar 

  • Maugin G.A. and Epstein M., (1991), The Electroelastic Energy-momentum Tensor, Proc. Roy. Soc. Lond., A433, 299–312.

    Article  MathSciNet  MATH  Google Scholar 

  • Maugin G.A. and Trimarco C., (1991), Pseudo-momentum and Material Forces in Electromagnetic Solids, Int. J.Appl. Electromagn. Mat., 2, 207–216.

    Google Scholar 

  • Maugin G.A. and Trimarco C., (1991), Pseudo-quantité de mouvement et milieux élastiques inhomogènes, C.R.AcadSci.Paris, II - 313, 851–856.

    Google Scholar 

  • Maugin G.A. and Trimarco C., (1992), Pseudo-momentum and Material Forces in Nonlinear Elasticity: Variational Formulations and Application to Brittle Fracture, Acta Mechanica, 94, 1–28.

    Article  MathSciNet  MATH  Google Scholar 

  • Maugin G.A. and Trimarco C., (1993), Material Conservation Laws in Continuum Mechanics and the Electrodynamics of Continua, in: Advances in Modern Continuum Mechanics, Ed. G. Ferrarese, pp. 131–149, Pitagora, Bologna.

    Google Scholar 

  • Maugin G.A. and Trimarco c., (1995), The Dynamics of Configurational Forces at Phase-Transition Fronts (70th Anniversary of J.L.Ericksen), Meccanica, 30, 605–619.

    Article  MathSciNet  MATH  Google Scholar 

  • Maugin G.A. and Trimarco C., (1995), Dissipation of Configurational Forces in Defective Elastic Solids, Arch.Mech. (Poland), 47, 81–99.

    MathSciNet  MATH  Google Scholar 

  • Maugin G.A. and Trimarco C., (1995), Configurational Forces and Coherent Phase-transition Fronts in Thermoelastic Solids (IUTAM Symp., Nottingham, 1994), in: Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics (A.J.M. Spencer Anniversary Volume), Eds. A. H. England and D. F. Parler, pp. 345–350, Kluwer, Amsterdam.

    Google Scholar 

  • Maugin G.A. and Trimarco C., (1997), Driving Force on Phase-transition Fronts in Thermoelectroelastic Crystals, Mathematics and Mechanics of Solids, 2, 199–214

    Article  MathSciNet  MATH  Google Scholar 

  • Norris, A.N., The energy of a growing elastic surface. Int. JSolids Structures, 36, 5237–5252.

    Google Scholar 

  • Nowacki J. P., Trimarco C. (1990): Note on thermal inclusion in elastic dielectric material. Atti Sem. Mat. Fis. Univ. Modena, XXXVIII, 371–378.

    MathSciNet  Google Scholar 

  • Sabir M. and Maugin G.A., (1996), On the Fracture of Paramagnets and Soft Ferromagnets, Int.J.Non-linear Mechanics, 31, 425–440.

    Article  MATH  Google Scholar 

  • Trimarco C. (1989): On the electrostatics of a rigid homogeneous isotropic and dielectric. Int. J. Engng. Sci., 27, 1569–1579.

    Article  MathSciNet  MATH  Google Scholar 

  • Trimarco C. (1992): The electric capacitance of a rigid dielectric structure. Int. J. of Solids and Structures, 29, 1647–1655.

    Article  MathSciNet  MATH  Google Scholar 

  • Trimarco C. (1994): The Toupin-Mindlin Theory of Dielectrics in The Light of View of Mossotti’s Idea. Bull. of Polish Academy of Sciences, 42, n. 3, 429–438.

    Google Scholar 

  • Trimarco C. (1999): Microscopic Variables and Macroscopic Quantities. In: Geometry, Continua and Microstructures, Série Mathématique: Travaux en cours, Ed. G.A. Maugin, pp. 121–129, Herrmann, Paris.

    Google Scholar 

  • Trimarco C. (1999): Hamiltonian versus Lagrangian Forms. In: Monographs and Surveys in Pure and Applied Maths series, 103–108, Chapman and Hall/CRC, ed.G.Iooss, O.Guès, A. Nouri.

    Google Scholar 

  • Truesdell C.A., and Noll W., (1965), Nonlinear Field Theories of Mechanics, in: Handbuch der Physik, Bd.III/3, ed. S. Flügge, Springer-Verlag, Berlin.

    Google Scholar 

  • Truesdell C.A., and Toupin R.A., (1960), The Classical Theory of Fields, in: Handbuch der Physik, Bd.III/1, ed. S. Flügge, Springer-Verlag, Berlin.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Wien

About this chapter

Cite this chapter

Trimarco, C., Maugin, G.A. (2001). Material Mechanics of Electromagnetic Solids. In: Kienzler, R., Maugin, G.A. (eds) Configurational Mechanics of Materials. International Centre for Mechanical Sciences, vol 427. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2576-2_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2576-2_3

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83338-4

  • Online ISBN: 978-3-7091-2576-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics