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
Distribution Statement : APPROVED FOR PUBLIC RELEASE