Foundations of Solid Mechanics

  • Chapter
  • First Online:
Local and Nonlocal Micromechanics of Heterogeneous Materials
  • 948 Accesses

Abstract

A major problem in continuum mechanics consists of predicting the deformations and internal forces arising in a material body subjected to a given set of external fields such as the forces of pure mechanical nature, temperature, and electromagnetic fields. This chapter summarizes some of important definitions, relations, and methods commonly employed for the analysis of reformable media although, of course, many aspects of mechanical behavior are left unaccounted for in this approach and referring the unsatisfied reader to monographs in which a level of higher generality is adopted. However, it is hoped that sufficient details are given so that the reader can understand remainder chapters without constant reference to other books.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 213.99
Price includes VAT (Germany)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 267.49
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
EUR 267.49
Price includes VAT (Germany)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Atkin RJ, Fox N (1990) An Introduction to the Theory of Elasticity. Longman, London

    MATH  Google Scholar 

  2. Ball JM (1977) Convexity conditions and existence theorems in nonlinear elasticity. Arch Rational Mech Anal, 63:337-403

    Article  MathSciNet  Google Scholar 

  3. Barnett DM, Lothe J (1975) Dislocation and line charges in anisotropic piezoelectric insulators. Phys Stat Solids (b), 67:105–111

    Article  Google Scholar 

  4. Borisenko AI, Tarapov IE (1968) Vector and Tensor Analysis with Applications. Prentice-Hall, Englewood Cliffs, NY

    MATH  Google Scholar 

  5. Carlson DE (1972) Linear thermoelasticity. In: Truesdell C (ed) Flügge’s Handbuch der Physik VI a/2. Springer-Verlag, Berlin-Heidelberg-New York, 297–346

    Google Scholar 

  6. Eringen AC (2002) Nonlocal Continuum Field Theories. Springer-Verlag, New York

    MATH  Google Scholar 

  7. Fung YC (1965) Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  8. Green AE, Zerna W (1968) Theoretical Elasticity (2nd edn). Oxford University Press, Oxford

    MATH  Google Scholar 

  9. Gurtin ME (1972) The linear theory of elasticity. In: Truesdell C (ed) Flügge’s Handbuch der Physik VI a/2. Springer-Verlag, Berlin, 1–295

    Google Scholar 

  10. Kachanov LM (1971) Foundation of Theory of Plasticity. North-Holland, Amsterdam

    Google Scholar 

  11. Koiter WT (1960) General theorems for elastic-plastic solids. In: Sneddon IN, Hill IR (eds), Progress in Solid Mechan. North-Holland, Amsterdam, 165–221

    Google Scholar 

  12. Lubarda VA (2002) Elastoplasticity Theory. CRC Press, Boca Raton, FL

    MATH  Google Scholar 

  13. Lurie AI (1990) Nonlinear Theory of Elasticity. North-Holland, Amsterdam, The Netherlands

    MATH  Google Scholar 

  14. Martin JB (1975) Plasticity: Fundamentals and General Results. MIT Press, Cambridge, MA

    Google Scholar 

  15. Maugin GA (1988) Continuum Mechanics of Electromagnetic Solids. North-Holland, Amsterdam

    MATH  Google Scholar 

  16. Nye JF (1957) Physical Properties of Crystals. Oxford University Press, Oxford

    MATH  Google Scholar 

  17. Ogden RW (1972) Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids. Proc Roy Soc Lond, A328:567–583

    MATH  Google Scholar 

  18. Ogden RW (1997) Non-linear Elastic Deformation. Dover, Mineola, New York

    Google Scholar 

  19. Parton VZ, Kudryavtsev BA (1988) Electromagnetic Elasticity of Piezoelectric and Electrically Conductive Bodies. Nauka, Moscow

    Google Scholar 

  20. Sedov LL (1966) Foundations of the Non-Linear Mechanics of Continua. Pergamon Press, Oxford

    MATH  Google Scholar 

  21. Shermergor TD (1977) The Theory of Elasticity of Microinhomogeneous Media. Nauka, Moscow (In Russian)

    Google Scholar 

  22. Sirotin YuI, Shaskolskaya MP (1982) Fundamentals of Crystal Physics. Mir Publishers, Moscow

    Google Scholar 

  23. Sokolnikov IS (1983) Mathematical Theory of Elasticity (2nd edn). Robert E. Krieger, Melbourne

    Google Scholar 

  24. Talpaert YR (2002) Tensor Analysis and Continuum Mechanics. Kluwer, Dordrecht

    Book  Google Scholar 

  25. Teodosiu C (1982) Elastic Models of Crystal Defects. Academei, Bucuresty, Springer, Berlin

    Google Scholar 

  26. Ting TCT (1996) Anisotropic Elasticity. Theory and Applications. Oxford University Press, New York, Oxford

    Book  Google Scholar 

  27. Torquato S (2002a) Random Heterogeneous Materials: Microstucture and Macroscopic Properties. Springer-Verlag, New York, Berlin

    Book  Google Scholar 

  28. Truesdell CA (1991) A First Course in Rational Continuum Mechanics. (2nd edn). Academic Press, New York, 1

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Cite this chapter

Buryachenko, V.A. (2022). Foundations of Solid Mechanics. In: Local and Nonlocal Micromechanics of Heterogeneous Materials. Springer, Cham. https://doi.org/10.1007/978-3-030-81784-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-81784-8_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-81783-1

  • Online ISBN: 978-3-030-81784-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Navigation