Crumpling Explained

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.

Significance

The packing of a sheet by crumpling is a complex phenomenon that depends on material parameters and the packing protocol. Thus the crumpling behaviour of foil, paper and poly-membranes differs significantly and can be interpreted on the basis of material foldability.[3] The high compressive strength exhibited by dense crumple formed cellulose paper is of interest towards impact dissipation applications and has been proposed as an approach to utilising waste paper.[4]

From a practical standpoint, crumpled balls of paper are commonly used as toys for domestic cats.

Notes and References

  1. Cerda . Enrique . Chaieb . Sahraoui . Melo . Francisco. Mahadevan. L . Conical dislocations in crumpling . Nature . 1999. 401. 6748 . 10.1038/43395. 1999Natur.401...46C . 46–49. 4331085 .
  2. Cambou. Anne Dominique . Narayanan . Menon. Three-dimensional structure of a sheet crumpled into a ball.. Proceedings of the National Academy of Sciences . 2011 . 108 . 36 . 14741–14745. 1203.5826. 2011PNAS..10814741C. 10.1073/pnas.1019192108. 3169141 . 21873249. free .
  3. Habibi. M . Bonn . D. Effect of the material properties on the crumpling of a thin sheet.. Soft Matter . 2017 . 3 . 22 . 4029–4034. 10.1039/C6SM02817A . 28512658 . 2017SMat...13.4029H .
  4. Mechanical properties in crumple-formed paper derived materials subjected to compression. Heliyon. 2017 . 3 . 6. e00329 . 10.1016/j.heliyon.2017.e00329 . Hanaor . D.A.H. . Johnson . E.A. Flores . Wang . S. . Quach . S. . Dela-Torre . K.N. . Gan . Y. . Shen . L.. 28653042. 5477149. 2017Heliy...300329H. free .