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



Author: Jemal Guven, Martin Michael Mueller

Source: https://arxiv.org/







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