Crumpling an elastoplastic thin sphere

The phenomenon of crumpling is common in nature and our daily life. However, most of its properties, such as the power-law relation for pressure versus density and the ratio of bending and stretching energies, as well as the interesting statistical properties, were obtained by using flat sheets. This is in contrast to the fact that the majority of crumpled objects in the real world are three-dimensional. Notable examples are car wreckage, crushed aluminum cans, and blood cells that move through tissues constantly. In this work, we did a thorough examination of the properties of a crumpled spherical shell, hemisphere, cube, and cylinder via experiments and molecular-dynamics simulations. Physical arguments are provided to understand the discrepancies with those for flat sheets. The root of this disparity is found to lie less in the nonzero curvature, sharp edges and corner, and open boundary than in the dimensionality of the sample.