Guided buckling of elastoplastic spherical shells induced by indenters of various shapes

Abstract

Mechanical instability, such as buckling of films, plates and shells, has emerged as a viable means of functional shape morphing, and has attracted much attention. Despite the extensive studies, examples with elastoplastic double-curved shells are rare, primarily because of the difficulties in fabrication and the complexities involved in analyzing their underlying high nonlinearities in materials, geometry, and contact. Here we use ping pong balls as specimens to study the post-buckling behavior of thin elastoplastic shells compressed by circular and polygonal indenters via compression tests and finite element simulations. We show that, for circular indenters, the nucleation and evolution of the buckling patterns, i.e., s-cones, are strongly affected by the indenter size and the yield stress of the shell. We also show that plastically deformed s-cones can be formed via the compression of a polygonal indenter of proper size with respect to the shell. Our findings may shed new light on rationalizing this highly nonlinear process, and may provide design guidelines that circumvent the need for creating inhomogeneous materials or geometrical imperfections.