When using Return Mapping algorithm, I implement Newton–Raphson iteration to reach the value of plastic multiplier. I know that the total value of plastic multiplier should not be negative. But, what should I do if one increment of plastic multiplier in an iteration is negative. Should I stop iteration or continue or what?
https://onlinelibrary.wiley.com/doi/pdf/10.1002/%28SICI%291097-0207%2819960730%2939%3A14%3C2477%3A%3AAID-NME962%3E3.0.CO%3B2-E
To my best knowledge, during iterations it is possible to have negative plastic multiplier. Iteratrions in NR method leads to some non-realistic intermediate states and only final, "equilibried" state must fulfil every theoretical assumption.
Dear Megahed.
Let me introduce first. I work about 14 y with plastic zone analysis of plane framed structures. My software PPLANAV run based on NR, which mean solve some very simple problems, like columns, beams and portals.
After all this time, I didn't worked with bigger structures because of the consummed processing time, which becomes higher when you have many numerical data involved and many NR iteration too.
Saying this, I may ask you how numerically the computer arrived to this negative number? I guess that you must check it precisely, to guarantee that there is no mistake in your matrices, in the answers produced first. Therefore, it recommends to slow down and analyze.
How the computer program produced this answer? There is a possibility of any kind of buckling is involved or coupled? It is there any numerical bug? It is some interdependency between the tensors that lead to an negative value?
Actually, in a case of a simple supported steel beam with a single vertical load at the mid-length, after the plasticity has formed a potential zone where will be the collapse, but there is some little elastic part yet, hundreds of iterations happen till reach the end. Making a plot of its deformed shape, between two consecutive iterations, you will see it like a string, downward and upward. Therefore, the iterations of NR, trying to null the residual force vector, make this change of direction because the structure is very sensible at this time.
So, you must certify yourself that the unstability phenomena or the resistance limit are occurring at that point, that there is a sound explanation for this numerical correction. If this is the case, everything is fine. Otherwise, look to your code and search if there is no other thing producing the unespected answer.
Good luck.
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