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Modeling Material Symmetry

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Abstract

The variation of material properties with respect to direction at a fixed point in a material is called material symmetry.

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References

  • Chadwick P, Vianello M, Cowin SC (2001) A proof that the number of linear anisotropic elastic symmetries is eight. J Mech Phys Solids 49:2471–2492

    Article  MathSciNet  MATH  Google Scholar 

  • Cowin SC (1995) On the number of distinct elastic constants associated with certain anisotropic elastic symmetries. In Casey J, Crochet MJ (ed) Theoretical, experimental, and numerical contributions to the mechanics of fluids and solids—a collection of papers in honor of Paul M. Naghdi, Z Angew Math Phys (Special Issue) 46:S210–S214

    Google Scholar 

  • Cowin SC (1999) Bone poroelasticity. J Biomech 32:218–238

    Article  Google Scholar 

  • Cowin SC (2002) Elastic symmetry restrictions from structural gradients. In: Podio-Guidugli P, Brocato M (eds) Rational continua, classical and new—a collection of papers dedicated to Gianfranco Capriz on the occasion of his 75th birthday. Springer Verlag, New York. ISBN 88-470-0157-9

    Google Scholar 

  • Cowin SC (2003) Symmetry plane classification criteria and the symmetry group classification criteria are not equivalent in the case of asymmetric second order tensors. Chinese J Mech 19:9–14

    Google Scholar 

  • Cowin SC, Mehrabadi MM (1987) On the identification of material symmetry for anisotropic elastic materials. Quart J Mech Appl Math 40:451–476

    Article  MathSciNet  MATH  Google Scholar 

  • Cowin SC, Mehrabadi MM (1989) Identification of the elastic symmetry of bone and other materials. J Biomech 22:503–515

    Article  Google Scholar 

  • Cowin SC, Mehrabadi MM (1995) Anisotropic symmetries of linear elasticity. Appl Mech Rev 48:247–285

    Article  Google Scholar 

  • Fedorov FI (1968) Theory of elastic waves in crystals. Plenum Press, New York

    Book  Google Scholar 

  • Fraldi M, Cowin SC (2002) Chirality in the torsion of cylinders with trigonal material symmetry. J Elasticity 69:121–148

    Article  MathSciNet  MATH  Google Scholar 

  • Hull D (1981) An introduction to composite materials. Cambridge University Press, Cambridge

    Google Scholar 

  • Neville C (1993) Biology of fibrous composites. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Nye JF (1957) Physical properties of crystals. Clarendon, Oxford

    MATH  Google Scholar 

  • Rovati M, Taliercio A (2003) Stationarity of the strain energy density for some classes of anisotropic solids. Int J Solids Struct 40:6043–6075

    Article  MathSciNet  MATH  Google Scholar 

  • Shubnikov AV, Koptsik VA (1974) Symmetry in science and art. Plenum, New York

    Google Scholar 

  • Tarn JQ (2002) Stress singularity in an elastic cylinder of cylindrically anisotropic materials. J Elasticity 69:1–13

    Article  MathSciNet  MATH  Google Scholar 

  • Thompson W (Lord Kelvin) (1904) Baltimore lectures on molecular dynamics and the wave theory of light. Clay & Sons, London

    Google Scholar 

  • Wainwright SA, Biggs WD, Currey JD, Gosline JM (1976) Mechanical Design in Organism, Edward Arnold, London

    Google Scholar 

  • Weyl H (1952) Symmetry. Princeton University Press, Princeton

    MATH  Google Scholar 

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Cowin, S.C. (2013). Modeling Material Symmetry. In: Continuum Mechanics of Anisotropic Materials. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5025-2_4

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  • DOI: https://doi.org/10.1007/978-1-4614-5025-2_4

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-5024-5

  • Online ISBN: 978-1-4614-5025-2

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