The passage from memory functionals to Rivlin-Ericksen constitutive equations (Q1089208)

The approximation of a constitutive equation of the memory functional type by one of the Rivlin-Ericksen type is discussed in the context of shear flows of a Maxwellian fluid. In the usual integral expression for the shear stress at time t in a Maxwellian fluid, the range of integration is usually taken as (-\(\infty,t]\). It is shown that incorrect conclusions can be reached with regard to the possibility of approximations of the Rivlin-Ericksen type unless cognizance is taken of the fact that the integral is strictly the limit as \(t_ 0\to -\infty\) of one in which the range of integration is \([t_ 0,t]\).