Skip to main content
SpringerLink
Log in

Nonlinear Localized Effects in Micromechanics

  • Conference paper
Recent Developments in Micromechanics

  • 107 Accesses

Summary

A series of examples dealing with electromagnetic elastic solids or compo site structures is presented to illustrate some large classes of phenomena in micromechanics (mechanics of materials with a microstructure). These examples deal either with the phenomenon of nonlinear localized moving structures such as solitary waves in a magnetoelastic thin film, in martensitic alloys, or in a nonlinear elastic substrate coated with a thin film, or with cooperative interactions in microstructured media (multi-domains in a ferromagnetic deformable specimen or piezoelectric composites). These examples illustrate the richness of the subject matter while pointing to engineering applications in mechanics and materials science. Mathematical details are avoided.

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 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.

Similar content being viewed by others

References

  1. Berdichevskii, V., and Truskimovskii, L., Energy Structure of Localization, in: Local Effects in the Analysis of Structures, ed. P. Ladevèze, 1985, pp. 127–158, Elsevier, Amsterdam.

    Google Scholar 

  2. Berdickevskii, V., Variational Principles in Continuum Mechanics (in Russian), 1983, Nauka, Moscow.

    Google Scholar 

  3. Maugin, G.A., Solitons in Elastic Crystals Exhibiting Phase Transition, in: Nonclassical Continuum Mechanics, ed. R. Knops and A. Lacey, 1987, pp. 272–283, Cambridge University Press, Cambridge, U.K.

    Chapter  Google Scholar 

  4. Maugin, G.A., Continuum Mechanics of Electromagnetic Solids, 1988, North-Holland, Amsterdam.

    MATH  Google Scholar 

  5. Eringen, A.C., and Maugin, G.A., Electrodynamics of Continue, Two volumes, 1989, Springer-Verlag, New York.

    Google Scholar 

  6. Dodd, R.K., Eilbeck, J.C., Gibbon, J.D., and Morris, A.C., Solitons and Nonlinear Wave Equations, 1982, Academic Press, London.

    MATH  Google Scholar 

  7. Motogi, S., and Maugin, G.A., Effects of Magnetostriction on Vibrations of Bloch and Néel Walls, Physica Statu Solidi, Vol. 81a, pp. 519–532, 1984.

    Article  ADS  Google Scholar 

  8. Motogi, S., and Maugin, G.A., Magnetoelastic Oscillations of a Bloch Wall in Ferromagnets with Dissipations, Japanese J1. of Applied Physics, Vo1 23, pp. 1026–1031, 1984.

    Google Scholar 

  9. Maugin, G.A., and Miled A., Solitary Waves in Elastic Ferromagnets, Physical Review, Vol. B33, pp. 4830–4842, 1985.

    ADS  Google Scholar 

  10. Pouget, J., and Maugin, G.A., Solitons and Electroacoustic Interactions in Ferroelectric Crystals, Parts I and II, Physical Review, Vol. B30, pp. 5306–5325, 1985; and ibid, Vol. B31, pp. 4633-4651, 1985.

    ADS  Google Scholar 

  11. Maugin, G.A., and Pouget, J. Solitons in Microstructured Elastic Media-Physical and Mechanical Aspects in: Continuuum Models of Discrete Systems (5), ed. A.J.M. Spencer, 1987, PP. 115–137, A.A. Balkema, Rotterdam.

    Google Scholar 

  12. Maugin, G.A., Solitons in Elastic Crystals with a Microstrueture — Mathematical Aspects, in: Trends in Applications of Pure Mathematics to Mechanics, eds. E. Kröner and K. Kirchgässner, 1986, pp. 195–211, Springer-Verlag, Berlin.

    Chapter  Google Scholar 

  13. Rudyak, V.M., Barkhausen Effect, Soviet Physics Uspekhi, Vol.13, No.4, pp. 461–479, 1971.

    Google Scholar 

  14. Sabir, M., and Maugin, G.A., Microscopic Foundations of the Barkhausen Effect, Archives of Mechanics, Vol.40, pp. 829–841, 1988.

    MATH  MathSciNet  Google Scholar 

  15. Sabir, M., Phenomenological Modelling of Ferromagnetic Noise in Stressed Materials (in French), Thesis, U.P.M.C., Laboratoire de Modélisation en Mécanique, Paris, France, 1988.

    Google Scholar 

  16. Maugin, G.A., Sabir, M., and Chambon, P., Coupled Magnetomechanical Hysteresis in Ferromagnets: Application to Non-destructive Testing, in: Electromagnetomechanical Interactions in Solids and Structures, eds. Y. Yamamoto and K. Miya, 1987, pp. 255–264, North-Holland, Amsterdam.

    Google Scholar 

  17. Maugin, G.A., Coupled Magnetomechanical and Electromechanical Hysteresis Effects, in: Applied Electromagnetics in Materials, ed. K. Miya, 1989, PP. 3–18, Pergamon, Oxford.

    Google Scholar 

  18. Bassiouny, E. Ghaleb, A.F., and Maugin, G.A., Thermodynamical Formulation for Coupled Electromechanical Hysterisis Effects, Part I to IV, Int. J. Engng. Sci., Vol. 26, pp. 1279–1295 and 1297-1306, 1988; ibid, Vol. 27, pp. 975-987 and 989-1000, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  19. Maugin, G.A., and Bassiouny, E., Continuum Thermodynamics of Electro-Mechanical Hysterisis Effects, in: Continuum Mechanics and Its Applications, eds. G.A.C. Graham and S.K. Malik, 1989, pp.225–235, Hemisphere Publ. New York.

    Google Scholar 

  20. Pouget, J., Nonlinear Dynamics of Lattice Models for Elastic Media, in: Physical Properties and Thermodynamical Behaviour of Minerals, ed. E.K. Salje, 1988, pp. 359–401, D. Reidel, Dordrecht.

    Google Scholar 

  21. Cadet, S., and Maugin, G.A., Modelling of Twins Propagation by Nonlinear Waves in Martensitic Alloys (in French), D.R.E.T. Final Report N° 87/1487/DRET/DS/SR2, UPMC, Laboratoire de Modélisation en Mécanique, Paris, France, 1989.

    Google Scholar 

  22. Maugin, G.A., and Cadet, S., Existence of Solitary Waves in Martensitic Alloys, Wave Motion (submitted in, 1989).

    Google Scholar 

  23. Falk, F., Martensitic Domain Boundaries in Shape Memory Alloys as Solitary Waves, J. Physique, Vol. C4, pp. 203–208, 1982.

    Google Scholar 

  24. Falk, F., Landau-Ginzburg Theory of Static Domain Walls in Snap-Memory Alloys, Zeit.Physik, Vol. B51, pp. 177–185, 1983.

    Google Scholar 

  25. Falk, F., Laedke, E.W., and Spatschek, K.M., Stability of Solitary-Wave Pulses in Shape-Memory Alloys, Physical Review, Vol. B36, pp. 3031–3041, 1987.

    ADS  Google Scholar 

  26. Hadouaj, M., and Maugin, G.A., Une onde solitaire se propageant sur un substrat élastique recouvert d’un film mince, C.R. Acad. Sci. Paris, Vol. II-309, 1989.

    Google Scholar 

  27. Maugin, G.A., Linear and Nonlinear SH Surface Acoustic Waves, in: Surface Waves in Solids and Layered Structures, ed. M. Borisov, 1990, World Scientific, Singapore.

    Google Scholar 

  28. Hadouaj, H., and Maugin, G.A., Solitary Surface Transverse Waves on an Elastic Substrate Coated with a Thin Film, Physica: D (submitted in, 1990).

    Google Scholar 

  29. Roseau, M., Vibrations in Mechanical Systems, 1987, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  30. Turbe, N., and Maugin, G.A., On the Linear Piezoelectricity of Composite Materials, Math. Methods in Applied Science (submitted in, 1989).

    Google Scholar 

  31. Telega, J.J., Piezoelectricity and Homogenization, in: Continuum Models and Discrete Systems (6), ed. G.A. Maugin, 1990, Vol. 2, Longman, London.

    Google Scholar 

  32. Pouget, J., and Maugin, G.A., Electroacoustic Echoes in Piezoelectric Powders, J.Acoust. Soc. America, Vol 71, pp. 941–954, 1983.

    Google Scholar 

  33. Maugin, G.A., Collet, B., and Pouget, J., Nonlinear Wave Propagation in Coupled Electromechanical Systems, in: Nonlinear Wave Propagation in Solids, ed. T.W. Wright, 1986, Vol. AMD. 77, pp. 57–84, A.S.M.E., New York.

    Google Scholar 

  34. Maugin, G.A., Collet, B., and Pouget, J., Evolution of Finite-Amplitude Waves in Elastic Crystals With a Microstructure, in: Problems of Nonlinear Acoustics, ed. V.K. Kedrinskii, 1988, Vol.1, pp.368–372, Publ. USSR Acad. Sci. Novosibirsk.

    Google Scholar 

  35. Maugin, G.A., Collet, B., Drouot, R., and Pouget, J., Nonlinear Electromechanical Couplings, (to appear 1991), Manchester University Press, Manchester, U.K.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Modélisation en Mécanique, associé au C.N.R.S. Université Pierre et Marie Curie, Tour 66, 4 place Jussieu, 75252, Paris, Cedex 05, France

    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. Dept. of Mechanical Engineering, McGill University, Montreal, QC, H3A 2K6, Canada

    D. R. Axelrad

  2. Institut für Theoretische Physik PN 7-1, Technische Universität Berlin, 1000, Berlin 12, Germany

    W. Muschik

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin, Heidelberg

About this paper

Cite this paper

Maugin, G.A. (1991). Nonlinear Localized Effects in Micromechanics. In: Axelrad, D.R., Muschik, W. (eds) Recent Developments in Micromechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84332-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-84332-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-84334-1

  • Online ISBN: 978-3-642-84332-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation