Varying the stiffness of inflating balloons via geometry*

When a thin elastic sheet is under tension, it stores elastic energy that resists local deformations. This everyday phenomenon can be observed while inflating a balloon - as the size of the balloon increases, the balloon gets stiffer. However, this simple relationship cannot be generalized to all shapes of inflatable structures. While a spherical balloon gets stiffer under inflation, a cylindrical balloon might get softer. Our findings suggest that whether a balloon gets stiffer or softer under inflation is closely dependent on the geometry of the inflating balloon. In particular, we find that the inflation-stiffness relationship is dependent on two parameters: the curvature of the balloon surface and the thickness of the elastic sheet that makes the balloon. In non-spherically shaped balloons where different regions have different curvatures, changing the ratio of these two variables modulates the stress distribution in the elastic material, which in turn controls the stiffness behavior of the balloons. These results give us a new control parameter to create systems with tunable stiffness, which could be applied in designing soft robots and other inflatable structures.