Thank you so much for your reply in detail and I really appreciate it! I can read the LSPP help docuement now.
However, I still have questions for J integtal in LSPP which confused me for long time. In the figure below, the left one is designed for Mode1 J integral and right one is designed for mode 2 J integal. The left one which is for Mode 1 has loading in position Y direction on the top and the total fixed boundary on the bottom. The right one which is for Mode 2 has loading in position X direction on the top and the total fixed boundary on the bottom.
Would you let me know if the crack opening direction vector for both case is (0,1,0) or (sin theta, cos theta,0)?
The vector (sin theta, cos theta,0) seem make more sense and agree with the docuement, but toturals(https://www2.dynamore.se/public/jernberg/jintegral.gif and www2.dynamore.se/public/jernberg/jintegral2.gif )above use (0,1,0) for not perfect crack example
Thank you so much!