The passage from memory functionals to Rivlin-Ericksen constitutive equations

Abstract

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 timet in a Maxwellian fluid, the range of integration is usually taken as (-∞,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 ast ₀→-∞ of one in which the range of integration is [t ₀,t].