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Harmonic Decomposition of Elastic Constant Tensor and Crystal Symmetry

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Transactions on Engineering Technologies

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Abstract

This paper presents a new outlook on harmonic decomposition method for elastic constant tensor. Harmonic decomposition method is developed in such a way that it is applied to anisotropic engineering materials exhibiting different crystal symmetry. The explicit results for each crystal symmetry types are presented. Numerical examples serve to illustrate and verify the developed method. This new representation of elastic constant tensor is compared with other theories such as orthogonal and non-orthogonal irreducible decompositions in literature. The results demonstrate that there are significant relationships between harmonic, non-orthogonal irreducible and orthogonal irreducible decomposition methods. While in harmonic and non-orthogonal irreducible decomposition methods, decomposition of total scalar part is not orthogonal. It is proposed that it is possible to make these parts orthogonal to each other.

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References

  1. J.F. Nye, Physical properties of crystals: their representation by tensors and matrices (Clarendon Press, Oxford, 1957)

    MATH  Google Scholar 

  2. E.T. Onat, Effective properties of elastic materials that contain penny shaped voids. J. Elast. 22, 1013–1021 (1984)

    MATH  Google Scholar 

  3. J.P. Boehler, A.A. Kirillov, E.T. Onat, On the polynomial invariants of the elasticity tensor. J. Elast. 34, 97–110 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. S.C. Cowin, Properties of the anisotropic elasticity tensor. Q. J. Mech. Appl. Mech. 42, 249–267 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  5. S. Forte, M. Vianello, Restricted invariants on the space of elasticity tensor. Math. Mech. Solids 11, 48–82 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. T.C.T. Ting, Q.C. He, Decomposition of elasticity tensors and tensors that are structurally invariant in three dimensions. Q. J. Mech. Appl. Mech. 59, 323–341 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. X. Zheng, Identification of symmetry planes in weakly anisotropic elastic media. Geophys. J. Int. 170, 468–478 (2007)

    Article  Google Scholar 

  8. B.D. Annin, N.I. Ostrosablin, Anisotropy of elastic properties of materials. J. Appl. Mech. Tech. Phys. 49, 998–1014 (2008)

    Article  MathSciNet  Google Scholar 

  9. Y.I. Sirotin, Decomposition of material tensors into irreducible elements. Kristallografiya 19(5), 909–915 (1974)

    Google Scholar 

  10. J. Jerphagnon, D. Chemla, R. Bonneville, The description of the physical properties of condensed matter using irreducible tensors. Adv. Phys. 8, 633–671 (1970)

    Google Scholar 

  11. D.L. Andrews, W.H. Ghoul, Irreducible fourth-rank Cartesian tensors. Phys. Rev. A 25, 2647–2657 (1982)

    Article  Google Scholar 

  12. Ç. Dinçkal, A new decomposition method for elastic constant tensor to study the anisotropy of construction materials; tool steel and rock types. Elixir Int. J. Appl. Math. 39, 5090–5092 (2011)

    Google Scholar 

  13. G. Backus, A geometrical picture of anisotropic elastic tensors. Rev. Geophys. Space Phys. 8, 633–671 (1970)

    Article  Google Scholar 

  14. R. Baerheim, Harmonic decomposition of the anisotropic elasticity tensor. Q. J. Mech. Appl. Mech. 46, 391–418 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  15. S. Forte, M. Vianello, Symmetry classes for elasticity tensors. J. Elast. 43, 81–108 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ç. Dinçkal, On the mechanical and elastic properties of anisotropic engineering materials based upon harmonic representations, in Proceedings of the World Congress on Engineering 2013, WCE 2013, 3–5 July 2013. Lecture Notes in Engineering and Computer Science, London, UK (2013), pp. 2177–2183

    Google Scholar 

  17. J.M. Brown, E.H. Abramson, R.J. Angel, Triclinic elastic constants for low albite. Phys. Chem. Miner. 33(4), 256–265 (2006)

    Article  Google Scholar 

  18. H. Landolt, R. Börnstein, M.M. Choy, K.H. Hellwege, A.M. Hellwege, Numerical Data and Functional Relationships in Science and Technology, New Series, Group III (Crystal and Solid State Physics), vol. 11 (Springer, Berlin, 1979)

    Google Scholar 

  19. H. Özkan, L. Cartz, in AIP Conference 1973, AIP Conference Proceedings, 1974, vol. 17, p. 21

    Google Scholar 

  20. Y.-M. Cheong, H.-K. Jung, Y.-S. Joo, S.-S. Kim, Y.-S. Kim, Dynamic elastic constants of Weld HAZ of SA 508 CL.3 steel using resonant ultrasound spectroscopy. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47(3), 559–564 (2000)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Çankaya University, Eskişehir yolu, 29.km, 06810, Yenimahalle, Ankara, Turkey

    Çiğdem Dinçkal

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  1. Çiğdem Dinçkal
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Correspondence to Çiğdem Dinçkal .

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Editors and Affiliations

  1. Department of Multimedia Engineering, College of Engineering, Mokpo National University, Mokpo, Jeonnam, Korea, Republic of (South Korea)

    Gi-Chul Yang

  2. Unit 1, 1/F IAENG Secretariat, International Association of Engine, Hong Kong, Hong Kong SAR

    Sio-Iong Ao

  3. Department of Applied Mathematics and Computing, Cranfield University, Cranfield, Bedfordshire, United Kingdom

    Len Gelman

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Dinçkal, Ç. (2014). Harmonic Decomposition of Elastic Constant Tensor and Crystal Symmetry. In: Yang, GC., Ao, SI., Gelman, L. (eds) Transactions on Engineering Technologies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8832-8_14

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  • DOI: https://doi.org/10.1007/978-94-017-8832-8_14

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-8831-1

  • Online ISBN: 978-94-017-8832-8

  • eBook Packages: EngineeringEngineering (R0)

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