How a Sheet Crumples

This simulated cube was made by cutting and joining a flat sheet of ideal elastic material. We test the strength of such objects by pushing symmetrically inward on the corners until the structure buckles. Color indicates amount of movement during buckling. Shading shows the elastic energy of the buckled state: buckling energy is concentrated in two unequal zones along the edges. The buckling strength qualitatively increased by the interplay of bending and stretching deformation in the sheet. A thin cube like this is arbitrarily stronger than e.g. a thin cylinder of the same material. Both the equilibrium energy and the buckling strength follow predicted power laws in the sheet thickness. Analogous strength is expected for randomly crumpled structures.

Crumpled sheets and puckered sheets like this cube are light, strong, and easy to make. They can sustain large deformations without catastrophic failure. Exploiting these newly demonstrated scaling laws will improve the design of future structural materials.

For the latest developments on our crumpling work, see the Forced Crumpling web site.