Rigid, perfectly plastic material behaviour corresponds to an initial range where deformations are null, independently on the level of applied stress. This is true until a level of stress σ0 (known as yield stress) is reached. Above this point, strains in the material increase indefinitely at constant stress. As a consequence, yield stress is the only parameter needed for a full description of this behaviour.
The mechanical simple model equivalent to this theoretical behaviour is a mass W sliding on an horizontal plane without inertial effects. Displacement is null if a load under a limit value (σ0) is applied. This force is dependent on the friction coefficient. Once this limit value is reached, the mass slides on the plane under a constant force. If the load applied is removed (the material is unloaded), the strain level reached remains as plastic (permanent) strain.
The simplest way to represent this mechanical system is by means of a friction plane defined by a constant σ0.