Skip to main content
SpringerLink
Log in

Dyadic method for tensor functions

  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

In this paper, we discuss tensor functions by dyadic representation of tensor. Two different cases of scalar invariants and two different cases of tensor invariants are calculated. It is concluded that there are six independent scale invariants for a symmetrical tensor and an antisymmetrical tensor, and there are twelve invariants for two symmetrical tensors and an antisymmetrical tensor. And we present a new list of tensor invariants for the tensor-valued isotropic function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Segel LA. Mathematics applied to continuum mechanics. New York: Macmillan Publishing Co., 1977

    MATH  Google Scholar 

  2. Zheng QS. On the representations for isotropic vector-valued, symmetric tensor-valued and skew-symmetric tensor-valued functions.Int J Engng Sci. 1993, 31: 1013–1024

    Article  MATH  Google Scholar 

  3. Jeffreys H, Swirles B. Methods of Mathematical Physics. Third edition. Cambridge: Cambridge University Press, 1999

    Google Scholar 

  4. Zheng QS. Theory of representations for tensor functions—A unified invariant approach to constitutive equations.Appl Mech Rev, 1994, 47: 545–587

    Article  MATH  Google Scholar 

  5. Pennisi S, Trovato M. On the irreducibility of Professor G.F. Smith's representations for isotropic functions.Int J Engng Sci, 1987, 25: 1059–1065

    Article  MATH  MathSciNet  Google Scholar 

  6. Boehler JP. On irreducible representations for isotropic scalar functions.ZAMM, 1977, 57: 323–327

    MATH  MathSciNet  Google Scholar 

  7. Huang YN, Luo XP, Ching ESC. A discussion about scalar invariants for tensor functions.Acta Mech Sinica, 2000, 16(1): 35–40

    Article  MathSciNet  Google Scholar 

  8. Huang YN, Luo XP. Discussion about the scalar invariants of representation theory for tensor functions.Acta Mech Sinica, 1999, 31(5): 504–509 (in Chinese)

    MathSciNet  Google Scholar 

  9. Smith GF. On isotropic functions of symmetric tensor, skew-symmetric tensors and vectors.Int J Engng Sci, 1971, 9: 899–916

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Turbulence Research, Department of Mechanics and Engineering Science, Peking University, 100871, Beijing, China

    Huang Yongnian & Lu Hao

Authors
  1. Huang Yongnian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lu Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The project supported by the Special Funds for Major State Basic Research Project “Nonlinear Science” and the National Basic Research Project “The Several Key Problems of Fluid and Aerodynamics”

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yongnian, H., Hao, L. Dyadic method for tensor functions. Acta Mech Sinica 18, 398–406 (2002). https://doi.org/10.1007/BF02487791

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02487791

Key words

Search

Navigation