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From the same paper as the previous image.
Citation no. 7 is:
[7] R.M.F. Paulo, F. Teixeira-Dias, R.A.F. Valente, Numerical simulation of aluminium stiffened panels subjected to axial compression: Sensitivity analyses to initial geometrical imperfections and material properties, Thin-Walled Structures, 62 (2013) 65-74.
“Local buckling” means “buckling of the panel skin between adjacent stringers”.
“Non-linear post-buckling region” means that the effective average axial stiffness of the panel skin is reduced because it is locally buckled, and the amplitude and axial wavelength of those local buckles is changing with increasing axial load.
Also, the entire panel starts bending as the axial load is increased because its axial neutral axis has shifted due to the skin being in its locally post-buckled state.
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