# Stress during unloading in FEM simulation of an elasto-plastic truss element

I am simulating the behaviour of a single bar composed of two node points by fixing one point and applying a force on the oder node with $$F_x = 1$$ and fixing $$u_y=0$$. I am assuming the material to behave elasto plastic with isotropic hardening.

My loading simulation for $$F_x = 0$$ to $$F_x = 1$$ with increment $$1/10$$ seems to be okay, my unloading process with same increment size is somehow weird. Maybe I am wrong but the stress should be $$0$$ for $$F_x = 0$$ again, right?.

• The thing that you are seeing here if you correctly formulated it, just showing you a typical elasto-plastic material behavior. When you go to plastic deformation region you have some permanent deformation or strain that will remain there even if you remove the load, so it's pretty normal to have a non-zero strain when your force is zero. – Alone Programmer Mar 17 '20 at 3:40
• Hey @AloneProgrammer, a non-zero strain when force is zero i clear for me. But how about a non-zero stress when force is zero? (Under the assumption the starting stress is zero) – LoveFrootLoops Mar 17 '20 at 6:47
• Maybe this has to do with the rheological model (check the model on Figure 1.b: researchgate.net/publication/…). In this model, above the yield stress you will have a remaining stress because the slider prevent the spring (only the one connected in parallel to the slider) returning to its original position which creates a permanent stress even after unloading. – Gustavo Costa Mar 17 '20 at 10:34
• @LoveFrootLoops That's called residual stress :) – Alone Programmer Mar 17 '20 at 13:27
• Theresore it seems to be normal? I just used a single truss element with an external force (i.e. traction) in one direction. For the elasto plasticity I used the a return mapping algorithm. – LoveFrootLoops Mar 17 '20 at 16:01