Mechanics of interconnected balloon networks

We investigate the mechanical stability of an array of interconnected thin balloons made from hyperelastic material that are filled with incompressible fluid. Each individual balloon has a nonmonotonic relation between the volume of enclosed fluid and the pressure difference between the inside and the outside of the balloon. While an individual balloon is unstable in the region with the negative slope on the pressure-volume diagram, such state of a balloon can get stabilized when it is interconnected with other balloons. We will present conditions that have to be satisfied for the mechanical stability for the whole network of balloons. Furthermore, we will discuss the dynamics of unstable configurations, which may exhibit an interesting sequence of liquid redistributions between the connected balloons, such that the volumes of balloons change nonmonotonically, before they settle in a new stable state.