While knowing about these models is part of a good theoretical understanding of viscoelasticity (including knowing full well that these models, like all models, have limitations while still being useful), this can also be helpful when explaining viscoelasticity of people not trained in the subject. Mechanical/civil/aeronautical/... engineers and physicists catch on quickly, while electrical engineers can struggle. Fortunately, this struggle can easily be resolved by using mechanical-electrical analogies. A dashpot is analogous to a resister - energy is irrecoverably lost, while a spring is analogous to a capacitor as they both store energy. Viscoelasticity is simply an RC-circuit. I've made this analogy to electrical engineers many times and it works quite well.
But the analogy can be problematic at times. Electrical engineers also work with another basic circuit element, an inductor. Inductors resist the change of electrical flow by taking advantage of a nearby magnetic field. While mass/inertia/momentum can be considered analogs to inductance and we can describe a flowing polymer in unsteady conditions as an RCL circuit, the next element is where the analogy completely breaks down.
The next element? Beyond the resistor, capacitor and inductor? Maxwell (him again) first described those three as basic, circuit elements back in the 1800's, often using the electromechanical analogy described above. And for the longest time, those three elements were all that were known to exist, at least as passive devices. However, in 1971, Prof. Leon Chua, using symmetry arguments, proposed a forth basic circuit element - the memristor. This device, showing both a memory and resistance (hence the name), would show decreasing resistance as more current had flowed through the device, and it would also remember what its resistance was when the device was turned off. After restarting the element, the resistance would be the same as before. Changing the direction of current flow would reset the device to its initial resistance. As with the inductor, all of this is possible by a coupling the current to a nearby magnetic field.
Going from theory to practice took some 37 years. Or did it? Apparently a controversy exists. I'm not in any position to say who's right and who's wrong. Regardless of the physical existence of the device, it exists theoretically. But even trying to describe a mechanical analog of a memristor is complicated. HP Senior Fellow Stan Williams describes it as:
" An analogy for a memristor is an interesting kind of pipe that expands or shrinks when water flows through it. If water flows through the pipe in one direction, the diameter of the pipe increases, thus enabling the water to flow faster. If water flows through the pipe in the opposite direction, the diameter of the pipe decreases, thus slowing down the flow of water. If the water pressure is turned off, the pipe will retain it most recent diameter until the water is turned back on. Thus, the pipe does not store water like a bucket (or a capacitor) – it remembers how much water flowed through it."And I further doubt that a polymeric analog of a memristor exists. While the whole idea of decreasing resistance with flow is quite analogous to shear thinning, the analogy fails on two fronts: polymers will lose the decreased viscosity upon cessation of flow (the rate of such loss being related to "the" relaxation time of the polymer), and switching flow directions will not reset the viscosity. Thank goodness, as dynamic mechanical analysis, where rheologists measure viscosity by imposing oscillatory shear on a sample, would not exist if it did.
Like all analogies, there are limits on their applications and if pushed too far, they break down. The analogy of a memristor to any part of a non-Newtonian fluid is just not going to happen, regardless of whether or not a memristor actually exists.