I am trying to reproduce the benchmark test "Single edge notched specimen under tension" to simulate crack propagation using phase field (AT2 model) with meshless radial basis function collocation method (LRBFCM). While following all the prescribed steps, I still cannot reproduce the results. I have solved the same test case with FENICS, but using LRBFCM, the phase field diffuses toward the upper and lower corners instead of propagating in a straight line as it should. I have tried many things, like

• Increasing the node density.
• With/without splitting the strain energy density.
• Decreasing the loading increment 100-1000 times (as compared to the benchmark test).
• Using different combinations of the boundary conditions.

I have solved the benchmark named "single-element test" successfully, and my model works well (for which the analytical solution is present in the literature, and my results match exactly the analytical solution).

Also, I have tested my mechanical model separately with an arbitrary phase field and compared the results with FENICS, which are in good agreement, but when I try to simulate the real case, the crack diffuses instead of propagating.

During simulations, while checking the convergence criteria, the simulation converges in a maximum of 2 steps in LRBFCM, whereas in FENICS, when the maximum value of the phase field exceeds 0.5, it takes many iterations for convergence.

I am struggling a lot and have been working on this problem for more than a year now; if any of the experts have any ideas, it would be highly appreciated if anyone could give me some suggestions on how to tackle this problem.

It will be highly appreciated. I am looking forward to your prompt response.

PS: I am solving the system of equations implicitly in a staggered form.