We study pneumatically inflated membranes indented by rigid indenters of different sizes and shapes. When the volume of the inflated membrane is beyond a critical value, a symmetric deformation mode becomes unstable and the system follows a path of asymmetric deformation. This bifurcation is analysed analytically for a two-dimensional membrane with either a line or plane indenter for which the stable deformation path is determined by computing the total system potential energy of different configurations. An axisymmetric membrane with indenters of different shapes and sizes is further investigated numerically. In this case, a cylindrical indenter can always trigger bifurcation while a small spherical indenter tends to be encapsulated rather than induce an asymmetric deformation mode. This result suggests that the observed bifurcation behaviour can be actively tuned and even triggered selectively by tuning indenter shape and size. We also demonstrate the effects of friction and biased bifurcation analytically through the example of a two-dimensional membrane with a line indenter.

我们研究了由不同尺寸和形状的刚性压头压入的充气膜。当膨胀的膜的体积超过临界值时，对称变形模式变得不稳定，并且系统遵循非对称变形的路径。对于具有线压头或平面压头的二维膜，可以对该分叉进行分析性分析，通过计算不同配置的总系统势能，可以确定其稳定的变形路径。数值研究了具有不同形状和大小的压头的轴对称膜。在这种情况下，圆柱形压头总是会触发分叉，而小的球形压头则倾向于被封装而不是引起不对称的变形模式。该结果表明，通过调整压头的形状和尺寸，可以主动地调整观察到的分叉行为，甚至可以选择性地触发它。我们还通过带有线压头的二维膜的示例分析性地证明了摩擦和偏分叉的影响。