The plane strain condition is satisfied when breath, b » h, the depth of the bar.
Find a stress system, e.g. σ = 0 in the length of the bar where there is the notch, σ = 2k elsewhere.
Therefore, for a breadth b, P = 2khb = load = stress × area
Postulate a suitable simple deformation pattern.
Assume yielding by slip on 45º shear planes with shear yield stress k. Let displacement along shear plane AB = δx.
Then internal work done = , where the force is acting on the shear plane AB.
Distance moved by the external load
So, here we obtain the same result for the upper bound and lower bound is the true failure load, the load required to cause plastic flow.