Thank you very much for your presentation. Would you mind explaining why in minute 25 you directly assumed that the dot product was not going to be greater than zero? The angle between the stress increment direction and the plastic strain increment was less than 90°.
If I understand your question, the point of that is to show that you *cannot* have the situation of an increment of stress that has some portion in the yield surface normal direction and yet puts you back inside the yield surface.
Hello Mark. Thanks for the videos, I have been enjoying them thoroughly. In the video AEM 648-10 Drucker's Postulates, around time 18.24 mins, there is an portion where you project one stress point inside of a monotonic stress strain curve onto the curve. Got a bit confused by this as I was wondering if such a stress state is possible (that stays inside the monotonic curve), my thought was that the stress states should follow the curve. Can you please comment, many thanks
I agree with you Sunil Job. And btw even the stress state can be transferred like the video showed, the Drucker postulate seems can not hold if the yield stress state at the softening branch is smaller than the elastic stress state (sigma star).
I have to say I've seen the normality rule described in a number of places and I've never really found the explanation that helpful. It's always stated that it satisfies the maximum plastic work, but why does the work have to be maximum?
I don't have access to my references at this time, but although the maximum dissipation postulate implies the normality flow rule, you are free to choose another flow rule (see non-associated flow rules). My feeling though is that there are some thermodynamic arguments (i.e. entropy) that could be made for maximum plastic dissipation--and, the normality flow rule tends to work well.
please doctor i am a beginner in plasticity and i have a question whats i understand is that if i have a stress state inside the yield surface it will be in the elastic range and if the stress state touch the surface it will begin to yield the question is as the material is hardening the yield surface is expanding so does the stress state always stay on the surface itself as they are both increasing together or the stress touch it once then it goes away from it while the material yielding and surface expanding ?
Hi Muhammad, yield surface (YS) plasticity requires the stress state to either be inside the YS or on it. This is called the consistency condition. The YS may either expand or translate or otherwise move depending on the hardening rule. I believe these ideas are explained in the other videos I have made. You may want to watch them, but I highly recommend reading books and taking a course on the subject.
Thank you for very nice explanation.
Thank you very much for your presentation. Would you mind explaining why in minute 25 you directly assumed that the dot product was not going to be greater than zero? The angle between the stress increment direction and the plastic strain increment was less than 90°.
If I understand your question, the point of that is to show that you *cannot* have the situation of an increment of stress that has some portion in the yield surface normal direction and yet puts you back inside the yield surface.
Hello Mark. Thanks for the videos, I have been enjoying them thoroughly. In the video AEM 648-10 Drucker's Postulates, around time 18.24 mins, there is an portion where you project one stress point inside of a monotonic stress strain curve onto the curve. Got a bit confused by this as I was wondering if such a stress state is possible (that stays inside the monotonic curve), my thought was that the stress states should follow the curve.
Can you please comment, many thanks
I will have to take a look, but I believe that was for an elastic unloading.
I agree with you Sunil Job. And btw even the stress state can be transferred like the video showed, the Drucker postulate seems can not hold if the yield stress state at the softening branch is smaller than the elastic stress state (sigma star).
I have to say I've seen the normality rule described in a number of places and I've never really found the explanation that helpful. It's always stated that it satisfies the maximum plastic work, but why does the work have to be maximum?
I don't have access to my references at this time, but although the maximum dissipation postulate implies the normality flow rule, you are free to choose another flow rule (see non-associated flow rules). My feeling though is that there are some thermodynamic arguments (i.e. entropy) that could be made for maximum plastic dissipation--and, the normality flow rule tends to work well.
Wonderful course Professor! I am learning so much. I would like to inquire as to which level of study is this? Masters, PhD?
Yes, plasticity is typically a graduate level course. Happy studies!
please doctor i am a beginner in plasticity and i have a question
whats i understand is that if i have a stress state inside the yield surface it will be in the elastic range and if the stress state touch the surface it will begin to yield the question is as the material is hardening the yield surface is expanding so does the stress state always stay on the surface itself as they are both increasing together or the stress touch it once then it goes away from it while the material yielding and surface expanding ?
Hi Muhammad, yield surface (YS) plasticity requires the stress state to either be inside the YS or on it. This is called the consistency condition. The YS may either expand or translate or otherwise move depending on the hardening rule. I believe these ideas are explained in the other videos I have made. You may want to watch them, but I highly recommend reading books and taking a course on the subject.
@@mbarkey.mechanics Thanks Doctor for fast reply im really appreciate your answer and for sure your great videos and teaching way.