Snap-Through Instability — Bistable Elastic Arch

A shallow elastic arch has two stable equilibria. As compressive load increases past a critical point, it snaps violently through to the other state — elastic instability.

STATE: UP (stable)
Critical load P_cr
P_cr = ±0.00
Deflection: 0.000
Snap-through occurs when the tangent stiffness ∂F/∂u → 0. The arch has a force-displacement curve with a "limit point" (fold). Beyond the limit load, no nearby equilibrium exists in the same branch — the system jumps.

Applications: snap-fit joints, MEMS actuators, compliant mechanisms, Venus flytraps (biological snap).