The discussion of the scale separation assumption of the FE² method: the buckling phenomena of fiber-reinforced composite structure

To clarify the applicable limit of the FE 2 method under conditions where scale separation is not obvious, this paper uses the FE 2 method to study and analyze the strong geometric nonlinear problems of fiber buckling. Keeping the geometric dimensions of the structure unchanged, the initial calculation arranges 32 representative volume elements (RVE) along the thickness direction, which are gradually decreased to 6 RVE. Results from these multiscale models are compared against full-scale refined finite element models. Displacement and stress relative errors are plotted against the macro-to-micro scale ratio (i.e., the number of RVEs along the thickness).