Physical Review E
mismatch strain, elastic sheets, curvature, geometry
Experiments have investigated shape changes of polymer films induced by asymmetric swelling by a chemical vapor. Inspired by recent work on the shaping of elastic sheets by non-Euclidean metrics [ Y. Klein, E. Efrati and E. Sharon Science 315 1116 (2007)], we represent the effect of chemical vapors by a change in the target metric tensor. In this problem, unlike that earlier work, the target metric is asymmetric between the two sides of the film. Changing this metric induces a curvature of the film, which may curve into a partial cylinder or a partial sphere. We calculate the elastic energy for each of these shapes and show that the sphere is favored for films smaller than a critical size, which depends on the film thickness, while the cylinder is favored for larger films.
Geng, Jun and Selinger, Jonathan V. (2012). Deformation of an Asymmetric Thin Film. Physical Review E 86(3). doi: 10.1103/PhysRevE.86.036602 Retrieved from https://digitalcommons.kent.edu/cpippubs/79