Maxwell memory function

The most often used relaxation modulus function is the multi-mode Maxwell memory function ... 

Solution. The relaxation modulus (memory function) Grit) for a Maxwell element is given by Equation 15.7b. For this particular strain history, Ay(/o) = +yo and Ay(/i) = —2y (remember, we need the increment, not the absolute value). Plugging these values into Equation 15.31 gives... 

The shear stress-relaxation modulus (memory function) for a Maxwell element is... 

An equation like 10.5, obtained from the Boltzmann principle by replacing the infinitesimal strain tensor by one that can describe a large deformation, is sometimes called a model of finite linear viscoelasticity . If the memory function in the rubberlike liquid is taken to be the relaxation modulus of a single Maxwell element [G(f) = Gq exp(f/T)], we obtain the special case of the rubber like liquid that we will call Lodge s equation this is shown as Eq. 10.6. 

Other possibilities exist to solve the frame invariant problem Cauchy-Maxwell equation uses the Cauchy tensor, C, which is also independent of the system of reference, the Lodge rubber-like liquid model uses the Finger tensor but contrarily to the Lodge model, it uses a generalized memory function ... 

This modification of the convected Maxwell model contains one constant G (an elastic modulus) and the non-Newtonian viscosity function rj y). It describes the shear-rate dependence of the viscosity perfectly and the first normal stress coefficient rather well. In steady elongational flow it gives an infinite elongational viscosity, and does not simplify properly in the linear viscoelastic limit. Nonetheless it has been found to be useful in exploratory flow calculations aimed at assessing the interaction of shear thinning and memory. 

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