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.
 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.
 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.