Well, hysteresis loop is the area under the curve or it represents the upward and downward movement od shear stress vs shear rate rheolograms and can predict texture degradation. You can consult my one paper on egg rheology where I showed hysteresis. Viscoelasticity is on the other hand material behavior and show how much solid-like or liquid-like property in terms of elastic and viscous modulus. For a perfect viscoelastic fluid both could be the same and if G' exceeds G'' then the solid-like property dominates. I have many papers you can find in research gate.

It is my pleasure to guide you if you do need more info.

Good luck.

Dear Dyako

Please see the article

Viscoelastic properties of concentrated dispersions in water of soy lecithin

M Manconib, J Aparicioa, A.O Vilaa, J Pendásc, J Figuerueloa, F Molinaa

Abstract

Viscoelastic properties of soy lecithin dispersions at 60, 120, 180 and 240 g l−1 in water have been studied as a function of ionic strength (NaCl concentrations in the range 10−5–10−2 mol l−1) and of preparation method (sonication, freezing–unfreezing). Viscosity measurements of sonicated dispersions in a rotatory viscometer show Newtonian and plastic (Bingham) behavior, whereas the frozen–unfrozen dispersions show a spectacular change in their viscoelastic properties, that is, a non-Newtonian behavior with pseudoplastic characteristics and rheopexy. These properties have been related to electrokinetic characteristics of the segregated vesicles in each case. A decrease in ζ-potential (in absolute value) of vesicles results on an increase in the hysteresis loop area of the parents dispersions.

2. The following work gives a good mathematical relationship

http://www.sciencedirect.com/science/article/pii/S1468121809000376

Well, hysteresis loop is the area under the curve or it represents the upward and downward movement od shear stress vs shear rate rheolograms and can predict texture degradation. You can consult my one paper on egg rheology where I showed hysteresis. Viscoelasticity is on the other hand material behavior and show how much solid-like or liquid-like property in terms of elastic and viscous modulus. For a perfect viscoelastic fluid both could be the same and if G' exceeds G'' then the solid-like property dominates. I have many papers you can find in research gate.

It is my pleasure to guide you if you do need more info.

Good luck.

http://www.tainstruments.com/pdf/literature/AAN016_V1_U_StructFluids.pdf

A hysteresis loop is related both to thixotropy and retarded viscoelasticity. The most interesting thing to do is to produce such a hystersis loop for two different acquisition time and to compare their shape.

Using creep ramps and inertia coupled elasticity, we have shown the relative effect of each phenomena on a range of food materials in the following paper:

http://www.researchgate.net/publication/226577013_Non-linear_viscoelasticity_and_temporal_behavior_of_typical_yield_stress_fluids_Carbopol_Xanthan_and_Ketchup/file/e0b4951dd09e3dcad1.pdf

Article Non-linear viscoelasticity and temporal behavior of typical ...

Viscoelastic will be exhibiting viscous-like as well as elastic characteristics and deviate from Hooke's law. These materials are those for which the relationship between stress and strain depends on time.

In elastic hysteresis, when a force applied to a body, the strain does not change simultaneously with stress, rather lag behind the stress. Due to this same strain does not occur for a given stress during loading and unloading.

In viscoelastic material, the area under the stress-strain curve during loading and unloading, is not same.