Numerical analysis of rubber balloons

The present paper deals with the inflation of two connected rubber balloons. This problem is known to exhibit instabilities and complex equilibrium paths. In some cases, the balloons inflate asymmetrically and equilibrium states with unequal radii take place. In this work, balloons are considered axisymmetric and discretized using an efficient B-spline discretization. The non-linear finite element procedure is associated with a stability and post-bifurcation analysis in order to determine singular points and to switch onto secondary equilibrium branches. The case of Mooney–Rivlin membranes is thoroughly investigated and the branching diagrams obtained are discussed in regards with the material parameters.