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Radius of Rolled-Up Trilayer

Using the principle of a bimetal strip on the nanoscale, rolled-up tubes with equilibrium radius can be fabricated by etching the layer below a prestrained multilayer. Here, we use three layers that are stacked on top of one other, with different eigenstrains , thicknesses , Young's modulus , and Poisson's ratio . Assuming mechanical equilibrium of bending forces and moments, the equilibrium radius can be determined.

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References
[1] G. P. Nikishkov, "Curvature Estimation for Multilayer Hinged Structures with Initial Strains," Journal of Applied Physics, 94(8), 2003 pp. 5333–5336. link.aip.org/link/?JAP/94/5333/1.
[2] P. Cendula, S. Kiravittaya, Y. F. Mei, Ch. Deneke, and O. G. Schmidt, "Bending and Wrinkling as Competing Relaxation Pathways for Strained Free-Hanging Films," Physical Review B, 79(8), 2009 p. 085429. prb.aps.org/abstract/PRB/v79/i8/e085429.
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