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Bounds on the anisotropic elastic constants
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Date
2008
Author
Dinçkal, Çiğdem
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In this thesis, mechanical and elastic behaviour of anisotropic materials are inves- tigated in order to understand the optimum mechanical behaviour of them in selected directions. For an anisotropic material with known elastic constants, it is possible to choose the best set of e¤ective elastic constants and e¤ective eigen- values which determine the optimum mechanical and elastic properties of it and also represent the material in a speci.ed greater material symmetry. For this reason, bounds on the e¤ective elastic constants which are the best set of elastic constants and e¤ective eigenvalues of materials have been constructed symbollicaly for all anisotropic elastic symmetries by using Hill [4,13] approach. Anisotropic Hooke.s law and its Kelvin inspired formulation are described and generalized Hill inequalities are explained in detail. For di¤erent types of sym- metries, materials were selected randomly and data of elastic constants for them were collected. These data have been used to calculate bounds on the e¤ective elastic constants and e¤ective eigenvalues. Finally, by examining numerical results of bounds given in tables, it is seen that the materials selected from the same symmetry type which have larger interval between the bounds, are more anisotropic, whereas some materials which have smaller interval between the bounds, are closer to isotropy.
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http://etd.lib.metu.edu.tr/upload/2/12609227/index.pdf
https://hdl.handle.net/11511/17465
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Graduate School of Natural and Applied Sciences, Thesis
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Ç. Dinçkal, “Bounds on the anisotropic elastic constants,” M.S. - Master of Science, Middle East Technical University, 2008.
