2007/12/06 by Jemal Guven, Martin Michael Mueller · 2 voices
Physics and Astronomy · #cond-mat.other #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/41/5/055203
published as J. Phys. A: Math. Theor. 41 (2008) 055203. · 20 pages, 1 figure
arxiv created 2007/12/06 · arxiv published 2007/12/06 · arxiv updated 2009/12/01
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.