Accession Number : AD0637520

Title :   ON THE INCLUSION OF THE COMPLETE SYMMETRY GROUP IN THE UNIMODULAR GROUP.

Descriptive Note : Technical rept.

Corporate Author : BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s) : Gurtin,M. E. ; Williams,W. O.

Report Date : JUN 1966

Pagination or Media Count : 26

Abstract : 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)

Descriptors :   (*GROUPS(MATHEMATICS), (*CONTINUUM MECHANICS), THERMODYNAMICS, ELASTIC PROPERTIES, EQUATIONS OF STATE, INEQUALITIES

Subject Categories : Theoretical Mathematics
      Mechanics
      Thermodynamics

Distribution Statement : APPROVED FOR PUBLIC RELEASE