INSTABILITIES IN THE FREE INFLATION OF A NONLINEAR HYPERELASTIC TOROIDAL MEMBRANE

摘要

We study an incompressible nonlinear hyperelastic thin-walled toroidal membrane of circular cross-section subjected to inflation due to a uniform pressure, comparing three elastic constitutive models (neo-Hookean, Mooney--Rivlin, and Ogden) and different torus shapes. A variational approach is used to derive the equations of equilibrium and bifurcation. An analysis of the pressure--deformation plots shows occurrence of the well-known limit point (snap-through) instabilities in the membrane. Calculations are performed to study the elastic buckling point to predict bifurcation of the solution corresponding to the loss of symmetry. Tension field theory is employed to study the wrinkling instability that, in this case, typically occurs near the inner {regions} of tori with large aspect ratios.