On The Principles of Equipresence and Unification
In 1960, Truesdell and Toupin  proposed that in formulating constitutive equations for phenomenological theories in which there is more than one constitutive equation, the following principle, which they named the Principle of Equipresence, must be satisfied: A variable present as an independent variable in one constitutive equation should be so present in all. In explaining the application of this principle, they state “Let it not be thought that this principle would invalidate the classical separate theories in the cases for which they are intended, or that no separation of effects remains possible. Quite the reverse: The various principles of invariance, stated above, when brought to bear upon a general constitutive equation have the effect of restricting the manner in which a particular variable, such as the spin tensor or the temperature gradient, may occur. The classical separations may always be expected, in one form or another, for small changes—not as assumptions, but as proven consequences of invariance requirements. The principle of equipresence states, in effect, that no restrictions beyond those of invariance are to be imposed in constitutive equations”.
KeywordsConstitutive Equation Phenomenological Theory Classical Separation Spin Tensor Specific Internal Energy
- C. Truesdell and R. Toupin, The classical field theories, Handbuch der Physik, Band III/I, Springer-Verlag, Berlin, 1960, §293Google Scholar
- C. Truesdell and W. Noll, The non-linear field theories of mechanics, Handbuch der Physik, Band III/3, Springer-Verlag, Berlin, 1965, §96Google Scholar
- R. S. Rivlin, J. Acoustical Soc. 40, 1213 (1966)Google Scholar
- R. S. Rivlin, Red herrings and sundry unidentified fish in nonlinear continuum mechanics, Inelastic Behavior of Solids, McGraw-Hill, New York, 1970Google Scholar
- A. C. Eringen, Nonlinear theory of continuous media, McGraw-Hill, New York, 1962, §44Google Scholar