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J integral for FGM

Submitted by Surendran M on

I have been trying to implement the J integral for an isotropic FGM based on the following paper

https://asmedigitalcollection.asme.org/appliedmechanics/article-abstract/72/3/351/459494/Consistent-Formulations-of-the-Interaction?redirectedFrom=fulltext

Please find enclosed the image which has the details.

I used equation 49 of the non-equilibrium formulation which is easier since it needs only the first order derivatives. However, my results don't match with benchmark results. In fact, it is close to the homogeneous case only. The equations and corresponding numerical form are given in the attached image. Can you point where its wrong?

 

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j_evaluation.png 101.97 KB