Ingeometry andtopology,crumpling is the process whereby a sheet ofpaper or other two-dimensionalmanifold undergo disordereddeformation to yield athree-dimensional structure comprising a random network ofridges andfacets with variable density. The geometry of crumpled structures is of interest to mathematicians studying topology.[1] Crumpled paper balls have been studied and found to exhibit surprisingly complex structures withcompressive strength resulting fromfrictional interactions atlocally flat facets between folds.[2] The unusually high compressive strength of crumpled structures relative to their density is of interest in the disciplines ofmaterials science andmechanical engineering.
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 formedcellulose paper is of interest towards impact dissipation applications and has been proposed as an approach toutilising waste paper.[4]
From a practical standpoint, crumpled balls of paper are commonly used astoys fordomestic cats.
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