Skip to main content

Mathematical Models in Mechanics of Deformable Solids

  • Chapter
  • First Online:
Treatise on Classical Elasticity

Abstract

The theoretical elements of a model in mechanics of deformable solids were described previously; it can be seen that these elements are generally closer to the ideal models of second order, but they must be supplemented by some data of experimental nature.

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

A. Books

  1. Boltzmann, L.: Populäre Schriften, 3rd edn. Leipzig (1925)

    Google Scholar 

  2. Carlslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids. Oxford University Press, Oxford (1948)

    Google Scholar 

  3. Green, G.: Mathematical Papers. London (1871)

    Google Scholar 

  4. Lamé, G.: Leçons sur la théorie mathématique de l’élasticité des corps solides. Paris (1852)

    Google Scholar 

  5. Neumann, F.: Vorlesungen űber die Theorie der Elasticität der festen Kőrper und des Lichtäters. Leipzig (1885)

    Google Scholar 

  6. Sokolnikoff, I.S.: Mathematical Theory of Elasticity, 2nd edn. McGraw-Hill, New York (1956)

    MATH  Google Scholar 

  7. Thomson, W.: (Lord Kelvin) Mathematical and Physical Papers, I–III, (1882, 1884, 1890)

    Google Scholar 

  8. Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity, 2nd edn., McGraw-Hill, New York

    Google Scholar 

B. Papers

  1. Adomit, G.: Determination of elastic constants of structured materials. In: IUTAM Symposium, 1967, Freudenstadt–Stuttgart, Mechanics of Generalized Continua, vol. 80 (1968)

    Google Scholar 

  2. Bekhterev, P.: Analiticheskoe issledovanie obobshchenogo zakona Guka (Analytical application of the generalized law of Hooke). J. Russkogo fiz.-khim. obshchestva, I. 7, 34 (1925), 8, 3 (1926)

    Google Scholar 

  3. Cauchy, A.L.: Mémoire sur les systèmes isotropes de points matériels. Mém. Acad. Sci. 22, 605 (1850)

    Google Scholar 

  4. Chentsov, N.G.: Issledovanie fanery, kak ortotropno plastinki (Applications of wood layers as orthotropic plates). Tekhn. zam, vol. 91 (1936)

    Google Scholar 

  5. Duhamel, J.-M.-C.: Mémoire sur le calcul des actions moléculaires développées par les changements de température dans les corps solides. Mém. Acad. savants étrangers, 5, 440 (1838)

    Google Scholar 

  6. Euler, L.: Determinatio onerum, quae columne gestare valent. Act. Acta Acad. Sci. Petrograd, 2, 121 (1780)

    Google Scholar 

  7. Green, G.: On the laws of reflection and refraction of light at the common surface of two non-crystallized media. Trans. Cambridge Phil. Soc. 7, 1 (1839)

    ADS  Google Scholar 

  8. Hoppman, W.H., Shahman, F.O.F.: Physical model of a 3-constant isotropic elastic material. Trans. ASME. Ser. E J. Appl. Mech. 32, 837 (1965)

    Article  ADS  Google Scholar 

  9. Joel, N., Wooster, W.A.: Number of elastic constants required in crystal elasticity. Nature 182, 1078 (1958)

    Article  ADS  Google Scholar 

  10. Krishnan, R.S., Rajagopal, E.S.: The atomistic and the continuum theories of crystal elasticity. Ann. der Physik 8, 121 (1961)

    Article  ADS  Google Scholar 

  11. Lamé, G.: Mémoire sur les surfaces isostatiques dans les corps solides homogènes, en èquilibre d’élasticité. J. Math. Pureset Appl. 6, 37 (1841)

    Google Scholar 

  12. Lamé, G., Clapeyron, B.-P.-E.: Mémoire sur l’équilibre intérieur des corps solides homogènes. Mém. prés. divers sav. étr., vol. 4 (1883)

    Google Scholar 

  13. Rabinovich, A.L.: Ob uprugikh postoyannykh i prochnosti anizotropnykh materyalov (On elastic constants and strength of isotropic materials). Trudy CAGI, vol. 582 (1946)

    Google Scholar 

  14. Teodorescu P.P.: Űber das kinetische Problem nichthomogener elastischer Kőrper. Bull. Acad. Pol. Sci., sér. Sci. Technol. 12, 867 (1964)

    Google Scholar 

  15. Teodorescu, P.P., Predeleanu, M.: Quelques considérations sur le problème des corps élastiques hétérogènes. In: Proceedings of IUTAM-Symposium. Non-Homogeneity in Easticity and Plasticity, Warszawa, 1958, Perganon Press, 31 (1959) [Bull. Acad. Pol. Sci., sér. Sci. Technol. 7, 81 (1959)]

    Google Scholar 

  16. Voigt, W.: Theoretische Studien űber die Elastizitätsverhältnisse der Krystalle. I, II. Abh. der Kőnigl. Ges. Wiss., Gőttingen, 34 (1887)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Petre P. Teodorescu .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Teodorescu, P.P. (2013). Mathematical Models in Mechanics of Deformable Solids. In: Treatise on Classical Elasticity. Mathematical and Analytical Techniques with Applications to Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2616-1_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-2616-1_4

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-2615-4

  • Online ISBN: 978-94-007-2616-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics