Xu and Needleman: Potential function in 3-D

Dear all,

I am improving the cohesive zone model in 2-D proposed by Y.F. Gao to simulate delamination between sub-micron thick films in 3-D. However, I did not find the potential function proposed by Xu and Needleman in 3-D. If you know it please tell me

Here is the potential function proposed by of Xu and Needleman in 2-D (in Y.F Gao’s paper)

The potential function proposed by Xu and Needleman in 3-D ??????

Thank you in advance

Do V.T