Elastic thin shells with large axisymmetric imperfection: from bifurcation to snap-through buckling

Abstract

Elastic thin shells are well-known for their highly unstable post-buckling, a response that exhausts their pressure bearing capacity and leads to catastrophic collapse. This paper examines elastic thin shells with a large axisymmetric imperfection that can escape the classical bifurcation of perfect spherical shells. We employ a shell theory formulation with exact expressions of the middle surface strains, curvature changes, and live pressure along with validating experiments and numerical simulations. The results show that a large axisymmetric imperfection in the form of a circular arc can induce snap-through buckling followed by a stable post-buckling that offers increasing resistance to pressure over a large change in volume. In addition, a sensitivity analysis on the role of defect geometry and shell radius to thickness ratio reveals the emergence of four buckling modes. For small imperfections, bifurcation buckling (mode 1) is dominant and resembles the typical dimple-like mode of perfect spherical shells. For larger imperfections, the shell attains the maximum pressure at the snap-through buckling where strain localization appears either within the imperfection (mode 2) or just below (mode 3). In the fourth mode, snap-through buckling precedes the attainment of the maximum pressure following a post-buckling path characterized by a large change of volume that makes the shell harder and stronger. These findings show that harnessing defect geometry and shell radius to thickness ratio can be effective in programming the post-buckling characteristics and transition between buckling modes, thus offering potential routes for the design of soft metamaterials with application to soft robotics and other sectors.