Curvature in compressed thin cylindrical shells approaching the isometric limit

The ability to manipulate surface elastic instabilities finds many applications in engineering smart interfaces, e.g. in fluid-structure interaction and micro-fabrication. We study the buckling of a thin cylindrical shell constrained to slide onto an inner non-deformable pipe. Our goal is to characterize the relationship between the shell thickness and the localization of stresses by using curvature measurements. First, we induce surface buckling by immobilizing one end of the shell and applying force to the other end. Then, we obtain a virtual reconstruction of the surface from 3D optical scanning and compute the Gaussian curvature for every point on the mesh. We find that as the shell gets thinner, the distribution of Gaussian curvatures becomes broader. Furthermore, measurements of areas enclosed by the parabolic lines around protruding vertices from the buckled surface show that the transitions between regions of positive and negative curvature are more localized. Finally, the Gaussian curvature reveals the formation of substructures within the lobes around the vertices. The localization results demonstrate that the cylindrical shell clearly evolves towards the isometric limit represented by the well-known Yoshimura pattern. However, the emergence of substructures indicates that this evolution is more complex than originally anticipated