Mapping inflation pathways for multiple connected balloons

Certain hyperelastic material systems, such as rubber balloons, exhibit an N-shaped pressure versus volume curve. This characteristic allows them to have two, unequal volume, stable solutions for a given pressure. Due to this property, it is well known that connecting two rubber balloons leads to instabilities and complex pathways. Taking inspiration from this phenomenon, we map the possible inflation/deflation pathways of connected hyperelastic balloons with different pressure curves, including those displaying bifurcation points and hysteresis. We then investigate methods for designing target pathways by determining the necessary pressure curve to reach them.