Attached you may find a picture for isotropic bilinear hardening up until the ultimate tensile strength. The first line is the elastic region while the second one is plastic. I couldn't understand that why is plasticity even a non-linearity in FEA? I mean if I just consider the graph below, then a point in a FEA model will just move over this graph only. If it switches from first line to the other, then there is just a change in the elastic modulus. If I am conducting a geometrically linear analysis, then how could inputting a material plasticity model, like the one showed below, make the analysis still be non-linear?
In the plastic range, the stress-strain relationship is non-linear as shown in the graph below. With consideration of geometric changes after yield, the true stress-strain curve (dotted line in the graph) shall be used instead of the normal curve, and non-linearity needs to be considered in the analysis.
Note: Due to the shrinking of section area and the ignored effect of developed elongation to further elongation, true stress and strain are different from engineering stress and strain.
$\delta_t = \delta(1 + \epsilon)$, and
$\epsilon_t = ln(1 + \epsilon)$