English

How paper folds: bending with local constraints

Other Condensed Matter 2008-01-24 v1 Soft Condensed Matter Statistical Mechanics

Abstract

A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns of a folded sheet of paper. The unstretchability of paper implies a constraint on the surface metric; bending is penalized by an energy quadratic in mean curvature. The local Lagrange multipliers enforcing the constraint are identified with a conserved tangential stress that couples to the extrinsic curvature of the sheet. The framework is illustrated by examining the deformation of a flat sheet into a generalized cone.

Keywords

Cite

@article{arxiv.0712.0978,
  title  = {How paper folds: bending with local constraints},
  author = {Jemal Guven and Martin Michael Mueller},
  journal= {arXiv preprint arXiv:0712.0978},
  year   = {2008}
}

Comments

20 pages, 1 figure

R2 v1 2026-06-21T09:51:18.804Z