We herein refine the strategy first formalized by Coleman and Noll for
deducing constitutive restrictions from the Clausius-Duhem inequality
. Specifically, we establish a key lemma that for certain materials al
lows the Coleman-Noll procedure to be carried out within just the clas
s of steady motions. By so shrinking the size of the process class nee
ded to employ the Coleman-Noll procedure, our lemma simultaneously enl
arges the class of real materials that we know must be mindful of cert
ain of the constitutive restrictions that descend from the principles
of thermodynamics. In particular, our lemma allows a thermodynamic ana
lysis, using just steady motions, of fluids of differential type-a con
stitutive class that the rheological community frequently lays down as
governing material response in steady motions, although it is ambival
ent about the use of such forms in more general motions. Thermodynamic
s is thus shown to deliver significant constitutive restrictions witho
ut anything being postulated for material response on nonsteady motion
s. (C) 1997 Elsevier Science Ltd.