Crumpling

In geometry and topology, crumpling is the process whereby a sheet of paper or other two-dimensional manifold undergoes disordered deformation to yield a three-dimensional structure comprising a random network of ridges and facets with variable density. The geometry of crumpled structures is the subject of some interest to the mathematical community within the discipline of topology.^[1] Crumpled paper balls have been studied and found to exhibit surprisingly complex structures with compressive strength resulting from frictional interactions at locally flat facets between folds.^[2] The unusually high compressive strength of crumpled structures relative to their density is of interest in the disciplines of materials science and mechanical engineering.