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Tensor function representations as applied to formulating constitutive laws for clinotropic materials

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Abstract

Crystals in the monoclinic system and composites reinforced with families of fibres in two non-orthogonal and mechanically non-equivalent directions are referred to as being clinotropic materials. In this paper, the complete and irreducible representations are established for clinotropic scalar-, vector-, second-order symmetric tensor- and second-order skew-symmetric tensor-valued functions of any finite number of second-order symmetric tensors, second-order skew-symmetric tensors and vectors. These representations constitute a rational basis for modelling the complex mechanical behaviour of clinotropic materials. As illustrative applications, the formulation of thermoelastic constitutive laws of clinotropic materials is developed.

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References

  1. Smith GF and Spencer AJM.Q J Mech Appl Math, 1970, 23: 489–504

    MATH  Google Scholar 

  2. Basista M.ZAMM, 1985, 65: 151–158

    MATH  MathSciNet  Google Scholar 

  3. Spencer AJM. The formulation of constitutive equations for anisotropic solids. In: Boehler JP ed.Mechanical Behaviour of Anisotropic Solids, Editions du CNRS (Paris), Martinus Nijhoff, The Hague, 1982. 2–26

    Google Scholar 

  4. Rogers TG. Yield criteria, flow rules, and hardening in anisotropic plasticity. In: Boehler JP ed. Yielding, Damage, and Failure of Anisotropic Solids. London: Mechanical Engineering Publications, 1990, 49–52

    Google Scholar 

  5. Lokhin VV and Sedov LI.Priklad Mat Mekh, 1963, 27: 393–417

    MathSciNet  Google Scholar 

  6. Boehler JP.ZAMM, 1979, 59: 157–167

    MATH  MathSciNet  Google Scholar 

  7. Boehler JP. Applications of Tensor Functions in Solid Mechanics. Springer-Verlag. 1987

  8. Zheng QS and Boehler JP.Acta Mechanica, 1994, 102: 73–89

    Article  MATH  MathSciNet  Google Scholar 

  9. Zheng QS and Spencer AJM.Int J Engng Sci, 1993, 31: 679–693

    Article  MATH  MathSciNet  Google Scholar 

  10. Zheng QS.Int Engng Sci, 1993, 31: 1013–1024

    Article  MATH  Google Scholar 

  11. Zheng QS.Int J Engng Sci, 1993, 31: 1399–1453

    Article  MATH  Google Scholar 

  12. Zheng QS, Betten J and Spencer AJM.Arch Appl Mech, 1992, 62: 530–543

    MATH  Google Scholar 

  13. Zheng QS.Proc Royal Soc Lond, Series A, 1993, 443: 127–138

    Article  MATH  Google Scholar 

  14. Pennisi S and Trovato M.Int J Engng Sci, 1987, 25:1059–1065

    Article  MATH  MathSciNet  Google Scholar 

  15. Eringen AC. Mechanics of Continua. Robert E. Krieger Pub Comp Inc, 1980

Download references

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Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, 100084, Beijing, China

    Zheng Quanshui

  2. University Joseph Fourier-Grenoble I, Domaine Universitaire, B. P. no 53X, F-38041, Grenoble Cedex, France

    J. P. Boehler

Authors
  1. Zheng Quanshui
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  2. J. P. Boehler
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Quanshui, Z., Boehler, J.P. Tensor function representations as applied to formulating constitutive laws for clinotropic materials. Acta Mech Sinica 10, 336–348 (1994). https://doi.org/10.1007/BF02486676

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  • DOI: https://doi.org/10.1007/BF02486676

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