Skip to main content

Part of the book series: Engineering Materials ((ENG.MAT.))

  • 295 Accesses

Abstract

A representation surface (RS from now on) is a simple graphical tool that helps understand how a physical magnitude depends on direction. Without worrying for the time being about the meaning of the two objects shown in the figure below, a RS conveys the information contained in the diagram on the left by means of the shaded surface on the right hand side. Most people find it easy to determine what the symmetries of the RS are, or in which directions it is elongated or shortened.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and 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
Hardcover Book
USD 54.99
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

Notes

  1. 1.

    This is a fine labeling arrangement for CEs. They do not represent fundamental laws imposed by Nature, but are more or less plausible quantitative statements that seem to passably or accurately reproduce the behavior of a material. Agreement with experiment is the key to the naming and survival of successful ones.

References

  1. Hinze, J.O.: Turbulence. McGraw-Hill, New York (1975)

    Google Scholar 

  2. Nye, J.F.: Physical Properties of Crystals. Oxford University Press, Oxford (1985)

    Google Scholar 

  3. Westin, C.-F., Maier, S.E., Mamata, H., Nabavi, A., Jolesz, F.A., Kikinis, R.: Processing and visualization for diffusion tensor MRI. Med. Image Anal. 6(2), 93–108 (2002)

    Article  Google Scholar 

  4. Barr, A.H.: Superquadrics and angle-preserving transformations. IEEE Comput. Graph. Appl. 1(1), 11–23 (1981)

    Article  Google Scholar 

  5. Haber, R.B.: Visualization techniques for engineering mechanics. Comput. Syst. Eng. 1(1), 37–50 (1990)

    Article  Google Scholar 

  6. Hotz, I., Feng, L., Hagen, H., Hamann, B., Joy, K., Jeremic, B.: Physically based methods for tensor field visualization. In: Proceedings of the Conference on Visualization’04, pp. 123–130. IEEE Computer Society (2004)

    Google Scholar 

  7. Jankun-Kelly, T.J., Mehta, K.: Superellipsoid-based, real symmetric traceless tensor glyphs motivated by nematic liquid crystal alignment visualization. IEEE Trans. Vis. Comput. Graph. 12(5), 1197–1204 (2006)

    Article  CAS  Google Scholar 

  8. Kindlmann, G.: Superquadric tensor glyphs. In: Proceedings of the Sixth Joint Eurographics-IEEE TCVG Conference on Visualization, pp. 147–154. Eurographics Association (2004)

    Google Scholar 

  9. Schultz, T., Kindlmann, G.L.: Superquadric glyphs for symmetric second-order tensors. IEEE Trans. Vis. Comput. Graph. 16(6), 1595–1604 (2010)

    Article  Google Scholar 

  10. Weickert, J., Hagen, H.: Visualization and Processing of Tensor Fields. Springer Science & Business Media, Berlin (2005)

    Google Scholar 

  11. Westin, C.F., Vilanova, A., Burgeth, B.: Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data. Springer, Berlin (2014)

    Book  Google Scholar 

  12. Newnham, R.E.: Properties of Materials: Anisotropy, Symmetry, Structure. Oxford University Press, Oxford (2005)

    Google Scholar 

  13. Tinder, R.F.: Tensor Properties of Solids: Phenomenological Development of the Tensor Properties of Crystals. Morgan & Claypool Publishers, San Rafael (2008)

    Google Scholar 

  14. Truesdell, C., Noll, W.: The Non-Linear Field Theories of Mechanics. Springer, Berlin (2004)

    Book  Google Scholar 

  15. Smith, R.R.: An Introduction to Continuum Mechanics: After Truesdell and Noll. Springer Science & Business Media, Berlin (2013)

    Google Scholar 

  16. Bird, B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena, 2nd edn. Wiley, New York (2002)

    Google Scholar 

  17. Öttinger, H.C.: Beyond Equilibrium Thermodynamics. Wiley, New York (2005)

    Book  Google Scholar 

  18. Prigogine, I.: Introduction to Thermodynamics of Irreversible Processes. Interscience Publishers, New York (1961)

    Google Scholar 

  19. De Groot, R., Mazur, P.: Non-Equilibrium Thermodynamics. North-Holland, Amsterdam (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Manuel Laso .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Laso, M., Jimeno, N. (2020). Introduction. In: Representation Surfaces for Physical Properties of Materials. Engineering Materials. Springer, Cham. https://doi.org/10.1007/978-3-030-40870-1_1

Download citation

Publish with us

Policies and ethics