I am familiar with the work of Rivlin in elasticity, Truesdell, Bird, Armstrong, etc. on rheology. However, I know there are other ways to build invariants than tensors and one can have objective evolution more generally than can be obtained by these methods. Is there evidence that the microscopic motions allowable in liquids will lead to equations governed by these constructions?
Dear Clifford Chafin, I see that you are orienting in state of art in this research problem. There are a lot of tensors in mechanics of solids and they have a wide enough possibilities for description of rhelogical phenomena. But some dissatisfaction in sense of adequate modelling of evolutional processes, really, is taking place. By this reason the conception of physical mesomechanics (see, please, papers of prof. Panin V. and co-workers) was proposed. This very common approach allows us to take into account the peculiarities of conjugate motion of microobjects (particles). All the best, Serge Shil'ko
In the field of 'granular media' there is a multitude of methods, from pure particle models, to purely continuous models. I find particle simulations particularly inpiring since they make clear that several happy accidents are required for allowing the particle to particle motion patterns to result in structures that can be described by constructs of differential geometry.
@Serge,
thanks for making me aware of this. Are there rheological versions of this as well? The stuff I found was for solids.
@Ulrich,
I started off in granular media and that is what led me to some recent work on rheology. Can you elaborate on these "happy accidents"? This is very intriguing.
What I ment is that looking to a simulation of streaming particles you often will not find stable correlation between the velocities or rotational velocities of nearby particles, and thus nothing like a mean flow. If however your particles have smooth and regular shapes and mild adheseve forces and are sufficiently densely packed they tend to behave like in a fluid flow. There is a huge variety in the conditions and it is hard to imagine that valid rules of useful generality can be formulated. Here we are definitively not in a realm of physics where simplicity is an indication of correctness.
@Ulrich,
this is interesting. I spent a long time doing gas kinetics and am interested in the more correlated dense limit. The problem is that I have found some corrections to rheology that are not describable in terms of the usual tensors and invariants constructed from the deviator in larger parcel averages. I'm trying to find out if others have found such a thing and even how to represent it in the context of current theory.
@Serge,
the group you point to does some very interesting research. Are there review articles or a way for me to get a handle on the scope of what they do?
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