Buckling of Shells - Predicting and Controlling Catastrophic Failure in Defect Sensitive Systems

It is notoriously difficult to systematically study the defect-sensitivity of buckling in shells, as these systems are extremely detail-dependent. Classical linear analysis of cylindrical shells overestimates their buckling loads, which has led to catastrophic failures. In an effort to overcome this challenge, we have developed a fully nonlinear framework inspired by research in turbulent flows. We capture the stability of shells by using lateral probing to measure their stability landscape. This enables unprecedented analysis and predictions of shell stability for shells with defects. We demonstrate the power of this experimental paradigm shift in addressing the shell stability problem by accurately predicting the strength of defective shells using a novel, non-destructive experimental ridge-tracking method. In our research, we chose to focus on commercial soda cans, such as Coke and Beer, as a model because they are widely used in our daily lives and representative of real industrially relevant shells. Additionally, we characterize the geometric imperfections of shells and image the radial deformations resulting from sub-critical loading. This reveals experimental evidence that localized failure in unmodified commercial cylindrical shells under an axial load is mediated by a bifurcation instability driven solely by the applied load. Geometric imperfections serve to localize the buckling mode in a manner which, surprisingly, is consistently predicted by numerical simulations of the loaded shell despite including only a partial description of its defects. These findings have practical implications for designing generic thin-shell structures. The picture that emerges is that while imperfections determine the buckling load of a shell, lateral probing provides a measure of the energy barrier to buckling at a particular spot. The entire nonlinear stability landscape and energy barrier can be directly, non-destructively measured through lateral probing, providing a viable method for characterizing the fundamental nonlinear processes that lead to catastrophic buckling in imperfect shells.