Archive for Rational Mechanics and Analysis

, Volume 74, Issue 2, pp 115–141 | Cite as

A formal description of representation theorems for constitutive functions

  • W. O. Williams
Article
Received:

Keywords

Neural Network Complex System Nonlinear Dynamics Electromagnetism Representation Theorem 
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References

  1. B.
    Bourbaki, N., Theory of Sets, Addison-Wesley Publishing Co., Reading, Mass. 1968.Google Scholar
  2. C.
    Coleman, B.D., On the use of symmetry to simplify the constitutive equations of isotropic materials with memory, Proc. Roy. Soc. A, 306, 449–476, 1968.ADSMATHGoogle Scholar
  3. O.
    Ore, O., Theory of equivalence relations, Duke Math. J., 9, 573–627, 1942.CrossRefMATHMathSciNetGoogle Scholar
  4. S.
    Szaz, G., Introduction to Lattice Theory, Academic Press, New York, 1963.Google Scholar
  5. TM.
    Truesdell, C., & H. Moon, Inequalities sufficient to ensure semi-invertibility of isotropic functions, J. Elasticity, 5, 183–189, 1975.MathSciNetGoogle Scholar
  6. W.
    Wang, C.-C., On a generalized representation theorem for constitutive relations, Arch. Rational Mech. Anal., 33, 1–25, 1969.CrossRefMATHMathSciNetGoogle Scholar
  7. WP.
    Weinberg, A.S., & A.C. Pipkin, Material symmetry restrictions on constitutive equations, Arch. Rational Mech. Anal., 17, 184–214, 1964.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • W. O. Williams
    • 1
  1. 1.Department of MathematicsCarnegie-Mellon UniversityPittsburgh

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