Hello everybody,
I am writing a UMAT for abaqus, a small strain perfect plasticty code. When i run my code for 4 node single element plain strain condition, i get a stress response higher than my yield stress. However, i get exactly the yield stress when a 3D single element is used. Hence, i am wondering what migth be the difference of same plasticty model according to 2D single element and 3D single element and why is 2D stress response is higher. I am adding a graph so that my question could be understood more easily. Thank you in advance!
Çağatay Kasar
Dear Cagatay Kasar,
Take into accoont that in plane strain state the stress tensor has additional non-zero component S33=S11/2. Therefore, in this case MISES=(0.75)0.5 S11 rather than S11 as in 3-D case. So, plasticity begins when S11=Syield in 3-D case, and when S11=(0.75)-0.5 Syield =1.1547 Syield in plane strain case.
Victor J. Аdlucky sir can you suggest me a source that i can find these type of computations and comparisons for plane stress/plane strain and 3D conditions?
Dear Cagatay Kasar,
I use the Russian edition of this book, but there is an English translation
Kachanov L. M. Foundations of the Theory of Plasticity
https://www.amazon.com/gp/product/B00Y30PZ4Y/ref=dbs_a_def_rwt_bibl_vppi_i2
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