Stress Localization of Thin Sheets in a Cylindrical Geometry

The ability to manipulate surface elastic instabilities finds many applications in engineering smart interfaces. We study the buckling phenomena of a thin cylindrical shell under axial compression that is constrained to slide onto an inner non-deformable pipe. Surface buckling is induced by immobilizing one end of the cylindrical shell and applying force to the other end. We study the geometry of the surface pattern, which is composed of rhombus shaped unit cells. We characterize the stress localization through shell thickness dependence and the out-of-plane deformation of the pattern after compression. Analysis of the curvature radii around the vertices of the unit cell shows that for thinner shells, the features get sharper suggesting that the stress is becoming more localized. Furthermore, as the thickness decreases, the distribution of the measured Gaussian curvature on the surface narrows around the zero mean indicating that the cylindrical shell is approaching the classical origami Yoshimura pattern.