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.
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Notes
- 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
Hinze, J.O.: Turbulence. McGraw-Hill, New York (1975)
Nye, J.F.: Physical Properties of Crystals. Oxford University Press, Oxford (1985)
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)
Barr, A.H.: Superquadrics and angle-preserving transformations. IEEE Comput. Graph. Appl. 1(1), 11–23 (1981)
Haber, R.B.: Visualization techniques for engineering mechanics. Comput. Syst. Eng. 1(1), 37–50 (1990)
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)
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)
Kindlmann, G.: Superquadric tensor glyphs. In: Proceedings of the Sixth Joint Eurographics-IEEE TCVG Conference on Visualization, pp. 147–154. Eurographics Association (2004)
Schultz, T., Kindlmann, G.L.: Superquadric glyphs for symmetric second-order tensors. IEEE Trans. Vis. Comput. Graph. 16(6), 1595–1604 (2010)
Weickert, J., Hagen, H.: Visualization and Processing of Tensor Fields. Springer Science & Business Media, Berlin (2005)
Westin, C.F., Vilanova, A., Burgeth, B.: Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data. Springer, Berlin (2014)
Newnham, R.E.: Properties of Materials: Anisotropy, Symmetry, Structure. Oxford University Press, Oxford (2005)
Tinder, R.F.: Tensor Properties of Solids: Phenomenological Development of the Tensor Properties of Crystals. Morgan & Claypool Publishers, San Rafael (2008)
Truesdell, C., Noll, W.: The Non-Linear Field Theories of Mechanics. Springer, Berlin (2004)
Smith, R.R.: An Introduction to Continuum Mechanics: After Truesdell and Noll. Springer Science & Business Media, Berlin (2013)
Bird, B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena, 2nd edn. Wiley, New York (2002)
Öttinger, H.C.: Beyond Equilibrium Thermodynamics. Wiley, New York (2005)
Prigogine, I.: Introduction to Thermodynamics of Irreversible Processes. Interscience Publishers, New York (1961)
De Groot, R., Mazur, P.: Non-Equilibrium Thermodynamics. North-Holland, Amsterdam (2013)
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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
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