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, we refer to regions of localization in shells 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 us to explore the frictional nature of the shell–indenter contact and characterize the relative properties of strain energy focusing, at different loci of localization. Our combined experimental and computational approach allows us to gain invaluable physical insight towards rationalizing this geometrically nonlinear process.