ON THE INCLUSION OF THE COMPLETE SYMMETRY GROUP IN THE UNIMODULAR GROUP.
BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS
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The complete symmetry of a group of a material is usually assumed to consist only of transformations which preserve the density of the material. In this paper it is shown that for a large class of materials this restriction is in fact a consequence of the Clausius-Duhen inequality. It is shown that elastic materials and a particular type of rate dependent materials fall into this class the proof extends to quasi-elastic materials and quasi-Rivlin-Ericksen materials of all orders. Finally certain restriction which the Clausius-Duhen inequality places on the individual stress, heat flux, entropy, etc. Symmetry groups are established for an elastic material. Author
- Theoretical Mathematics