This is a note of my current understanding.

When faced with a piece of material, that is by definition, useful matter, we always want to reproduce it in as large amount as possible. An in the next immediate step, we also wants to know the why and how about the usefulness (i.e. function) of this type of material, in order to mimic it and design similar but enhanced products. To understand the reason of materials function we look for none but the structure by default. I know no reason why we believe that functions must be caused by structures. Maybe this structure-function relationship principle in materials science is only an incarnation of the reductionism.

When investigating the structure-function relationship we of course split our effort twofolds, to describe exactly the structure, and to measure exactly the function. Experimental rheologists contribute mainly to the latter. In rheology we applied an external deformation field and measure the response (stress) of the sample. Generally we always apply an external field and measure the response of the materials to know any functions. A small enough external field trigger a field-strength independent response which we call linear, while larger field strength trigger a response dependent at least and not limited to the field strength, called nonlinear. We “love” linear responses because we can use a single materials function, the susceptibility χ(t) to predict the response to any form of external field. All these “linear”, “nonlinear” stuffs are theory of systems and signals; we in fact view the materials as systems and we always like the case when they are linear, causal and time-invariant.

Practically the external fields we like to apply to a sample are multifarious: electricity, magnetics, light, heat, etc. But when it comes to “soft matter” whose major fascination is the “softness”, giving a deformation field, i.e. rheology, is inevitably one of the main concern of soft matter research.

And the trouble of soft matter is, as a system, it is often “time-variant” and easily entering nonlinear regime, and the concept “soft matter” actually includes a very wide spectrum of materials with different structures. Now the phenomenological similarity reported by the experimental rheologists has become a big question for theorists; they have to find the generality among such varying structural features, for examples, by using the “glass” or “jamming” concepts. Sometimes simply finding a proper description of the method is difficult, for example the four-point correlation function chi₄ for describing dynamic heterogeinity.