Inflating balloons with patterned rigidity

We develop a method to obtain the equilibrium three dimensional shape of a thin heterogeneous elastic membrane when starting with an initially flat, two dimensional pattern of mixed inextensible and extensible materials. We investigate the effect that a small piece of inextensible material has when placed in between extensible material and vice versa. We then use these results to guide us into investigating ways of solving the inverse problem i.e. finding a pattern of materials of different stiffness in two dimensions so as to achieve a desired three dimensional target shape.