CRITICAL PRESSURES FOR THE BUCKLING OF THICK-WALLED SPHERICAL SHELLS UNDER UNIFORM EXTERNAL PRESSURE

Abstract

For isotropic incompressible hyperelastic materials the problem of determining the critical pressure at which a thick-walled spherical shell buckles when subjected to a uniform external pressure involves solving a fourth-order system of highly non-homogeneous ordinary differential equations. Closed-form solutions of this system are derived here for a particular hyperelastic material which has not been studied previously. These solutions are used to derive the buckling criterion, and numerical values are obtained for the resulting critical pressures. For thin shells these values are in agreement with classical thin-shell theory while for thicker shells close agreement is obtained with existing results for the neo-Hookean material. However for thin shells the predicted buckling mode is different from that given by previous authors. It can be shown from previously published experimental results on simple extension and simple compression that the new strain-energy function is a valid prototype for vulcanized rubber over a limited range of deformation and moreover that it agrees with the neo-Hookean theory for small strains.