The modelling of linear elastic, perfectly plastic behaviour is a combination of the 2 precedent models.
The initial part of the curve corresponds to a linear elastic behaviour described by the elastic constant E (and Poisson ratio). Once yield stress σ0 is reached the material behaves as plastic, flowing at a constant stress σ0.
The mechanical model used to describe this behaviour has a linear elastic spring with constant E and a friction plane with constant σ0 in series connection. The load along both elements is the same. It reflects an elastic deformation of the spring until the stress reference level of the friction plane is reached. Once this limit value is reached, displacement continues under constant load. If the system is unloaded the spring recovers its initial length, but the strain generated at the friction plane (plastic) remains permanent.