I´d like to know which method abaqus uses for nonlinear problems. I´m in doubt about it, I don´t know if it uses the total Lagrange or updated Lagrange. If somebody could help me, I appreciate.
If you consider "updated Lagrangian" formulation as updating the integration points coordinates after each loading increment in order to perform integration over the material volume, then....
...I think is it is both, depending on if you account for geometric nonlinearities (NLGEOM=ON) or not.
Though, if I am not mistaken, you will never find "updated Lagrangian" in Abaqus documentation.
it is clearly written in the doc that (at least) the small-strain shell elements use Total lagrangian strain in stresses. Finite membrane-strain elements are in corotational formulation.