Localization of deformation in thin shells under indentation

Abstract

We perform a hybrid experimental and numerical study of the localization of deformation in thin spherical elastic shells under indentation. Past a critical indentation, the deformation of the shell ceases to be axisymmetric and sharp points of localized curvature form. In plates, these sharp points are known as d-cones. By way of analogy, regions of localization in shells are referred to as s-cones, for 'shell-cones'. We quantify how the formation and evolution of s-cones is affected by the indenter's curvature. Juxtaposing results from precision model experiments and Finite Element simulations enables the exploration of the frictional nature of the shell-indenter contact. The numerics also allow for a characterization of the relative properties of strain energy focusing, at the different loci of localization. The predictive power of the numerics is taken advantage of to further explore parameter space and perform numerical experiments that are not easily conducted physically. This combined experimental and computational approach allows us to gain invaluable physical insight towards rationalizing this geometrically nonlinear process.