TY  - JOUR
ID  - Průša201222
T1  - On implicit constitutive relations for materials with fading memory
A1  - Průša, Vít
A1  - Rajagopal, K. R.
JA  - Journal of Non-Newtonian Fluid Mechanics
Y1  - 2012
VL  - 181–182
IS  - 0
SP  - 22
EP  - 29
SN  - 0377-0257
UR  - http://www.sciencedirect.com/science/article/pii/S0377025712001127
M2  - doi: 10.1016/j.jnnfm.2012.06.004
KW  - Convected coordinates
KW  - Implicit constitutive theory
KW  - viscoelastic fluids
N2  - Starting with an implicit constitutive relation between the stress and relative deformation gradient histories to describe the response of a fluid, and using the assumption of fading memory, we show that both rate type and differential type fluid representations can be obtained, as approximations in retarded motions, that have the same form as the Maxwell, Oldroyd-B, Rivlin–Ericksen, and other popular fluid models. This result provides further evidence that the recently proposed implicit constitutive framework provides a very robust and general methodology to describe fluid response. Thus, fluids defined through an implicit constitutive relation between the stress and relative deformation gradient histories can be seen as an appropriate generalization of the notion of simple fluids and rate type fluids.
ER  -