I'm struggling to find a good detailed reference explaining the Arc-length method or, more generally, Riks method and its derivations. I looked for the classical books in nonlinear mechanics (the ones by Crisfield, De Borst, Bathe, etc) but they're confusing for a beginner in nonlinear analysis. Thus, I'd like to request for references regarding the Arc-length method for systems of nonlinear equations. I'm not new to FEM and I'm aware of Newton-Raphson method but the problem I'm dealing with presents a snap-through behavior due to softening of the material.
I agree that Crisfield's book is not a clear place to start for this topic. Have you read the original paper by Riks, "An incremental approach to the solution of snapping and buckling problems", IJSS 1979? It is quite clear in my opinion. If you don't have access, I can send it to you. I believe the modification by Crisfield is widely used, and his paper "A fast incremental/iterative solution procedure that handles 'snap-through'", Computers & Structures 1981 is also clearly written. If you have any specific questions about implementation I can try to help.