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Abstract
We present a simple discrete formula for the elastic energy of a bilayer. The formula is convenient for rapidly computing equilibrium configurations of actuated bilayers of general initial shapes. We use maps of principal curvatures and minimum-curvature direction fields to analyze configurations. We find good agreement between the computations and an approximate analytical solution for the case of a rectangular bilayer. For more general shapes (simple polyiamonds), we find a range of typical bending behaviors: overall bending directions along longest and shortest dimensions, inward bending at corners, curvature intensification near boundaries, and conical bending and partitioned bending zones in some cases.
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Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA
Silas Alben
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Correspondence toSilas Alben.
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Communicated by: Anette Hosoi
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Alben, S. Bending of bilayers with general initial shapes.Adv Comput Math41, 1–22 (2015). https://doi.org/10.1007/s10444-014-9347-2
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