I am writting a code to simulate elasto-plastic behaviour of a 2D plane stress model.The finite element discretization is based on quadrilateral elements.My question is based on calculation of stresses. Suppose the the displacement solution is obtained at each node.Thus, for the calculation of the yield function do I have to calculate stresses at each Gauss point for every element obtaining a stress tensor at each GP and then calculate yield function? Is that procedure correct? Does the calculation of yield function or equivalent stresses refer to every element at every Gauss Point and further the elastic predictor steps and return mapping should be done for every GP?
Yes, the procedure is correct. Stress has be computed at every GP.
Usually, in each finite element the stress values are computed at the Gauss points (Barlow's points) because there the accuracy is the highest, and then the computed values are extrapolated to the nodes, because there we also know the node coordinate.
At each node you have a stress tensor values, that is, you may have up to 6 independent stress values (3 sigma, 3 tau) - in plane stress you only have 3 stresses, the other being zero.
Only then you can apply an equivalent stress criterion (von Mises) to convert the nodal multiaxial stress into an equivalent uniaxial stress
Is it necessary to extrapolate stresses at nodes?Can't work only with integration points?
You guessed correct. Obviously, the stresses are computed at GP and later interpolated for the nodes to obtain the yield function.
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