Secondary bifurcation buckling in material-extrusion manufactured stayed lattice cells: experimental detection and nonlinear analytical modeling

Stayed lattice unit cells (UCs) fabricated by material extrusion additive manufacturing (MEX-AM) exhibit enhanced load-carrying capacity due to the restraining effect of diagonal stays. However, accurately predicting their buckling and post-buckling behavior remains challenging, particularly when manufacturing-induced sagging of the stays is considered. In this study, an analytical model incorporating nonlinear spring elements is developed to represent the mechanical response of the stays, including the transition of stays from a non-active (slack) zone to an active (fully engaged) zone. The nonlinear spring behavior is calibrated by fitting an exponential function to the experimental force–displacement behavior of the stays. This model predicts an initial C-mode buckling followed by a secondary bifurcation into double-S-mode, which is experimentally validated using digital image correlation (DIC). The non-active zone primarily affects the amplitude of the C-mode: an increase in the non-active zone leads to a corresponding increase in the C-mode amplitude, while the critical loads associated with both the primary buckling and the secondary bifurcation remain unchanged. This finding is experimentally validated by tuning the printing parameters (bridge), demonstrating that the predicted influence of the non-active zone can be realized in practice. In addition, the column slenderness can influence the post-buckling behavior, with more slender configurations exhibiting a more stable post-buckling response. The proposed analytical framework enables efficient simulation of buckling and post-buckling behavior and becomes a key component of Make–Break–Simulate workflow. This approach facilitates the design of lattice structures with controlled and programmable buckling behavior, supporting applications requiring high strength-to-weight efficiency and targeted deformation mechanisms.