TY - JOUR
T1 - The shape and mechanics of curved-fold origami structures
AU - Dias, Marcelo A.
AU - Santangelo, Christian D.
PY - 2012/12
Y1 - 2012/12
N2 - We develop recursion equations to describe the three-dimensional shape of a sheet upon which a series of concentric curved folds have been inscribed. In the case of no stretching outside the fold, the three-dimensional shape of a single fold prescribes the shape of the entire origami structure. To better explore these structures, we derive continuum equations, valid in the limit of vanishing spacing between folds, to describe the smooth surface intersecting all the mountain folds. We find that this surface has negative Gaussian curvature with magnitude equal to the square of the fold's torsion. A series of open folds with constant fold angle generate a helicoid.
AB - We develop recursion equations to describe the three-dimensional shape of a sheet upon which a series of concentric curved folds have been inscribed. In the case of no stretching outside the fold, the three-dimensional shape of a single fold prescribes the shape of the entire origami structure. To better explore these structures, we derive continuum equations, valid in the limit of vanishing spacing between folds, to describe the smooth surface intersecting all the mountain folds. We find that this surface has negative Gaussian curvature with magnitude equal to the square of the fold's torsion. A series of open folds with constant fold angle generate a helicoid.
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U2 - 10.1209/0295-5075/100/54005
DO - 10.1209/0295-5075/100/54005
M3 - Article
AN - SCOPUS:84871293386
SN - 0295-5075
VL - 100
JO - EPL
JF - EPL
IS - 5
M1 - 54005
ER -