If a force, F, stretches a wire of length x and cross-sectional area A, to an elongation of Δx, the elastic potential energy per unit volume is:
u = (1/2) × (F/A) × (Δx/x)
But, (F/A) is stress, and (Δx/x) is the strain. Thus,
u = (1/2) × stress × strain
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