I tried to code this method and it diverges when the stiffness approach zero. As, calculating load vector coefficient ∆λ requires having inverse of the stiffness as shown in the attached photo (https://scholar.harvard.edu/files/vasios/files/ArcLength.pdf) .So do anyone have a solution to it
to verify a singular (zero stiffness) configuration, you may try other techniques to artificially inhibit divergence in your model's response.
As long as K_T is not singular, you should be able to get a solution with a good/quadratic convergence (assuming you are using full Newton method). K_T is singular at limit points, however there is a tiny chance that your algorithm directly hits these points during the path following- you can try to change the time step size even though I don't think this is the case. If your problem is complex such as in the case of high nonlinearities, line search quite helps with the convergence.
Arc Length Method has multiple versions. I think the Cylindrical version could help you. Please have a look at the following reference:
A Unified Library of Nonlinear Solution Schemes by Sofie E. Leon, Glaucio H. Paulino, Anderson Pereira, Ivan F. M. Menezes, and Eduardo N. Lages
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