The plane strain condition is satisfied when breath, b » h, the depth of the bar.
Lower-Bound:
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
Upper-Bound:
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.
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