What the difference between displacement and load control to solve the answer in a simulation? For example, is there different for initial strain increment when use displacement control or load control?
I think that there's no special treating of such simulation and Abaqus probably does not recognize whether the analysis is load or displacement controleed. Thus the initial increment should be the same. It is however much easier to obtain converged solution in case of highly nonlinear problems when the displacement control is used. Not because of different methods being used to solve governing equations - the approach is just better for nonlinear problems involving contact or stability loss.