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Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Sep;84(3 Pt 2):036603. Epub 2011 Sep 16.

Programmed buckling by controlled lateral swelling in a thin elastic sheet.

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Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.


Recent experiments have imposed controlled swelling patterns on thin polymer films, which subsequently buckle into three-dimensional shapes. We develop a solution to the design problem suggested by such systems, namely, if and how one can generate particular three-dimensional shapes from thin elastic sheets by mere imposition of a two-dimensional pattern of locally isotropic growth. Not every shape is possible. Several types of obstruction can arise, some of which depend on the sheet thickness. We provide some examples using the axisymmetric form of the problem, which is analytically tractable.


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