Thanks for your encouragement. It's intriguing to hear you using the word "calm" to describe the presentation. Perhaps it is true at a deeper level? Metaphorical?

@@polymerphysics2242 Much interesting!

The Perspective is available here:pubs.acs.org/doi/10.1021/acs.macromol.3c01952

Thanks. For a polymer researcher interested in mechanical behavior of polymer, I would say Nonlinear polymer rheology is the mother of everything else mechanical. It informed us very well about what polymers are made of...

@@polymerphysics2242 Totally agree. Actually I was not well trained in non linear since the classical approach always had some 'fear' to deal with the real effects of non-linearity. For this reason I'm really happy to have found your classes here because I also started to read your amazing book in this subject. My intention is to broad my knowledge with it, so I may apply it in my research of extrudable gel polymer blends for lithium ion batteries. Hope to see one of your lectures one day. Best, KA TOZZI

Amazingly, people who built the molecular theory for nonlinear polymer rheology did not seem to know the meaning of the most basic feature of nonlinearity: shear stress exhibits a maximum (overshoot). The concept of yielding is entirely foreign to polymer rheologists - how could a liquid yield? Henning Winter was an NSF director in mid 2000. He phoned me because he had my proposal on is desk and told me that "we learned in graduate school that the overshoot is some sort of nonlinearity". For anything, we don't understand, blame nonlinearity.

Amir, You have to read Kinloch's book on Fracture behavior of polymers to see how I view the subject differently. I nearly disagree with everything in that book, and we are collecting evidence to show why.

The best way to learn the meaning of TTS is to do it manually.

It's nice to hear from you. Where are you now? I use twitter and we have moved on to fracture mechanics. A video is coming.

Notification never alerted me concerning your question. Just see this now. Fantastic question. This is the most charming, intriguing and interesting point. Consider the extreme case where each LBS is straighten. What happens? Each occupy a cross-section of s and bear load, given by the chain tension f_ct. So you achieve maximum retractive stress: f_ct/s. The other limit is when LBSs are in their isotropic coiled state. It would occupy many units of s (the cross-section of a chemical bond) by folding back and forth. What is its contribution to the retractive stress? Only one f_ct by the definition of LBS being load-bearing strand.

I also talked about this subject in the lecture series (Lecture 12 of 29 lectures) on Nonlinear Polymer Rheology, starting 26th minutes: kzbin.info/www/bejne/poG1ipqHgLZmjNk emphasize a key concept of geometric condensation of chain network.

Hi Professor Nele, Get me know if you have trouble getting hold of a free ecopy of the book. I can send one to you. Best, SQ

The logic of Considere is questionable. Perhaps one ought to first find out how the tensile force would start to drop (i.e., identify the material physics responsible for it). To say that the force maximum implies necking misses point: the force decline is the effect (we should identify the structural/mechanical cause for the force decline) rather than the cause for neck. At two different levels of description, you see the cause and effect switched! Just say this comment and thought I should reply.

@@polymerphysics2242 there's much more than that, however the fact it's still mostly* valid. Is correct and it really does corresponds to the material point of necking. Also I would not refer it as force than Stress. Because it's uses True stress and strain by definition. Not just force. Because the force is not quite correctly determined in such way as the stress is. And yes in that sense the inclination/is corresponding to the localization of deformation in true sense and because I do quite a lot of testing I really can say it does and you might easily observe it. The facts Why's that and why there are quite a couple of mechanisms, which might be involved is the really tricky part. What Considere' did not take in account are reversible changes for instance. Not these elastic or plastic but recoverable inelastic. Therefore, it's relatively genius thing for most everyday used material and cases but not suitable for more complex materials or composites.

@@marijhorn there cannot be any confusion regarding force vs. stress. By definition, engineering stress is nothing but normalized (by initial cross-sectional area) total force. Indeed, I suppose that the force decline could arise from the specimen being non-uniform, either geometrically or structurally. I am not considerably such cases. For polymer melts, it is possible to rule out such a case, yet the engineering stress shows a peak. See the counter example in J. Rheol. 55, 1247 (2011); doi: 10.1122/1.3626416 - Figures 4 to 6 show force maxima without necking at all!

@@polymerphysics2242 will look at the article. Truly interested in to the results. The major problem in the theory is that it's working only with the plain (recalculated) stress-strain. Not True* (real true) cross section reduction. But even that even if corresponding to some particular response at the S-S curve it doesn't mean that place will be necessarily the ultimate necking area. Will look t the publication thanks.

@@polymerphysics2242 Not working with polymers myself, however regarding these data in 4-6 in above mentioned article my first guess would be some form of "natural drawn ratio" in action.. therefore getting first some gradual change in the polymers either by forming more uniformly elongated chains or some form of defect accumulation. The "similar" can be observed even for metallic materials. Regardless of that with engineering stress recalcualted to the "True stress" you imidietely switch these two peaks and the higher (and closer to the failure) truly corresponds to the Considere' criterion therefore the formation of final necking prior failure.

That's a recording of my talk on fracture mechanics of plastics at APS March meeting. It is perhaps copyright issue.

Professor could you kindly record a video on the future of polymer physics research, rheology research .. like what are the current trends, hot topics and where the research is headed?

The trend is up to the scientists in the polymer community to take. What I know is that given the importance of the mechanical aspects of polymeric materials, there is only a disproportionally small fraction of efforts on the topic. Why? In part, because the subject is challenge to study. Perhaps we are more ready to tackle it now because of the new understanding of nonlinear polymer rheology covered in the lectures. We are not going to wait. We proceed to apply and explore the processing-structure-property relationship. A good example is the story covered in the media: newatlas.com/materials/durable-new-bioplastic-boiling-liquids/

Teaching is my passion..., thanks for listening to it.

now lectures based on the book is available at kzbin.info/www/bejne/j5CZiIaehNSFbdU

If we don't know what polymer entanglement is, how can we begin to describe its response to externally imposed fast large deformation? The tube model offered us one way to think about chain entanglement. It does not question what causes a tube to undergo affine deformation, and therefore it cannot answer when the affine deformation ceases and irreversible deformation begins. We presented a second way to think about chain entanglement. Here at least we tried to explain where the affine deformation comes from. We also proposed the force imbalance as a mechanism for the affine deformation to terminate. Adam, you could propose a third way. When you do so, you want to address how the elastic deformation first emerges upon startup deformation presumably due to entanglement and how entanglement survives or not as the external deformation goes on. Keep thinking. Yes, the 1/3 scaling behavior can be understood in terms of the force imbalance idea, as shown in the class (Chapter 16 in the book).

now lectures based on the book is available at kzbin.info/www/bejne/j5CZiIaehNSFbdU