Instabilities in the free inflation of a nonlinear hyperelastic toroidal membrane

Abstract

Study on an incompressible nonlinear hyperelastic thin-walled toroidal membrane of circular cross-section subjected to inflation due to a uniform pressure is conducted in this work. Comparisons are made for three elastic constitutive models (neo-Hookean, Mooney-Rivlin, and Ogden) and for different geometric aspect ratios (ratio of the radius of cross-section to the radius of revolution). 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 membrane. Calculations are performed to study the elastic buckling point to predict bifurcation of solution corresponding to 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.