The role of boundary on equilibrium configuration of rotational symmetric gel sheets

In rotational symmetric gel sheets, we study the sheets with in-plane strain and deduce the equilibrium equations and the boundary conditions. The boundary is found to play an important role in the equilibrium configuration of the gel sheet. Compared to the sheet without a boundary, with a boundary the strain enlarges extremely. The domination between bending and stretching can be changed by the boundary. In gel sheets with a boundary, the forming mechanism of equilibrium configuration is different from the sheet without a boundary. The equilibrium configuration is governed by the cooperation of boundary, bending, and stretching rather than just the last two. Furthermore, we find that the boundary line tension γ cannot be omitted. If γ is ignored, the elastic energy roughly enlarges by 5%. Finally, we discuss the effects of γ and propose a way to measure it by the border radius.