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Energy release rate

cracking analyses in a bended sandwich beam

I'm studying cracking analyses in a three point loaded specimen of a composed beam.I'm using ANSYS and i want to create codes for estimation of J integral and energy release rate in the vicinity of crack tip.After that i'll calculate the stresses and strains fields,and then i can compare the equivalent fields i retrived using CTOD  and K(I,II,III) factors (according to ANSYS algorithm).

My problem is that I'd like to find a relationship between the above mentioned quantities(J,G)  with K(I,II,III)factors.

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