Crumpling
In geometry and topology, crumpling is the process whereby a sheet of paper or other two-dimensional manifold undergo 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 of interest to mathematicians studying 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
[edit | edit source]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.
References
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