condensed matter - Why the elastic limit of solid corresponds to a larger strain/extension than the limit of proportionality? - Physics Stack Exchange

In all the force-extension graphs I saw, the elastic limit corresponds to a larger extension than the limit of proportionality. Is this true for all cases? If so, what are the underlying reasons?

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Figure shows the graph of elastic potential energy U stored versus extension, for a steel wire Y= 2× 1011 Pa of volume 200 cc. If area of cross section A and original

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