Self-Buckling of Pressurized Cylindrical Tubes
We investigate the buckling of hollow cylindrical tubes subject to their own weight and internal pressure, inspired by the columnar cells of the palisade mesophyll in dicotyledon leaves which resemble pressurized cylindrical tubes. When the internal pressure in the cylinder is equal to the outside pressure, the problem is usually termed self-buckling, which has been studied extensively for solid rods, hollow cylinders, and thin cylindrical shells. Specifically, we perform FEM simulations and desktop-scale experiments to determine the instability thresholds for different geometrical parameters. We first test our models against self-buckling results without pressure for solid rods and hollow cylindrical tubes, and then proceed to determine the critical buckling pressure for a set of material and geometrical parameters. We find that positive internal pressures can stiffen cylinders that are unstable under their own weight, leading to an effective Young's modulus that we show scales linearly with the applied pressure. On the contrary, cylinders that are stable under self-weight, buckle under a negative pressure, resembling classical results on pressure-induced ring buckling. Our findings offer new insights on the interplay between gravity and pressure for the mechanical instability of hollow cylindrical tubes, which we hope will be useful for the study of both engineering and biological structures under similar loads.