Bifurcation, which alters the number and stability of equilibria in multistable systems, is the primary mechanism governing the formation of elastic sequential snap-through instabilities. However, to date, there is no general understanding of the multistable energy landscape organized by bifurcations underlying snap-through. Here, we conduct a theoretical, numerical, and experimental analysis of serial bistable planar curved beams widely proposed in the recent literature, developing numerical algorithms and experimental schemes to explore the bifurcation structures within the energy landscape. Such systems provide sufficient physical transparency, owing to their low dimension and clear interaction, making them ideal for the analysis of bifurcation structures. Two types of elastic sequential snap-through instability are discovered: competition-induced phase transitions, triggered by limit forces (switching fields) between units, and unit phase transitions, triggered by the equivalent stiffness of system variables within each unit. In our method, we propose a general tunable snap-through path design strategy for use in multistable systems, which can be extended to broader systems with interacting units. Importantly, by tuning stiffness properties and the limit force perturbations, custom-designed saddle-node bifurcation pairs and traverse-stable paths can be achieved, providing universal design rules for elastic sequential transitions.

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• Bifurcations
• Buckling
• Continuum mechanics
• Elastic deformation
• Mechanical metamaterials
• Phase transitions