Fracture Mecanics, dU/da = KI^2/E

Hi Experts,

It is me again, a Fracture Mechanics beginner. You know the expression of the released energe in the opening of a crack U = sigma^2/(2E)*pi*a^2 derived from a case that a rectangular plate stretched by a line of equal and opposite forces at each ends, and KI = sigma*sqrt(pi*a) is derived in the same (similar?) case. Then, from the above two expressions, the book got dU/da = KI^2/E OK, fine. However, the book uses dU/da = KI^2/E in another case that a system of equal and opposite forces applied to the crack surfaces. I think dU/da = KI^2/E can only be used in the case that the forces applied far away from the crack! Can you explain why.....

Thank you in advance.

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victor
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