Nonlinear convergence in FEA refine mesh, adjust solver, or modify material model

[Sophia_R]

I'm a mechanical engineer performing a finite element analysis on a complex composite structure, and I'm getting convergence issues with my nonlinear material model under specific loading conditions. I've refined my mesh in the high-stress regions, but the solution still oscillates or fails to converge. For experienced FEA users, what are your systematic troubleshooting steps for addressing nonlinear convergence problems, and how do you decide between further mesh refinement, adjusting solver settings, or revisiting the material model assumptions?