Consider two bars one rigid and the other deformable, acted upon by two equal and opposite point loads P as shown. In either of the cases, if we cut the beam from an imaginary section, then, to bring (say) the left part of the beams (obtained after cut) in equilibrium an equal and opposite force, equal to P, must be developed in that part of the beam.
In case (b), the intensity of these internal resistive forces developed on the section is called stress, and is equal to the internal resistive forces divided by the area.
In case (a), since the bar is rigid it doesn't undergo any deformation. Hence, there must be no stresses, since stresses appear to resist deformations. However, we see that even in (a) internal resistive forces are developed, and hence we can define their intensity via stress.
So, my question is, is there any stress in the rigid bar? If no, how am I to conceive the internal force developed in case (a)?