Non-linearity in rheology —an essay of classification

Different non-linear phenomena (such as non-Newtonian flow, large elastic deformations, instabilities of different types and many others) are the heart of rheology. Therefore many attempts were carried out to find quantitative, or at least qualitative, models of non-linear behavior. The general or perhaps most attractive way of developing rheological constitutive equations consists in the search for the most general method to describe everything in the framework of a single approach. Naturally, this leads to very complicated and ambiguous equations. Meanwhile, it is reasonable to try another way based on separating observed phenomena into different types depending on observed phenomena into different types depending on their physical origin. An attempt to propose such their physical origin. An attempt to propose such classification of nonlinear rheological effects is made.According to the assumed scheme three levels of non-linearity are distinguished. There is a group of phenomena which originate as a consequence of finite elastic deformations. This is weak non-linearity related to equilibrium properties of a matter. The second level can be characterized as strong non-linearity. It is related to reversible structure changes, developing in time and connected with changes in relaxation properties of a matter. This group of effects can be treated as kinetic phenomena. Lastly, the third level of non-linearity is connected with breaking or phase transitions induced by deformations. This leads to the most severe consequences and can be treated as effects of thermodynamic nature. It is shown that some well known rheological effects can be explained if we consider them as a superposition of non-linearity of different types.Presented as keynote lecture at the European Rheology Meeting, September 4–9, 1994, Sevilla, Spain