Dynamic inflation of non-linear elastic and viscoelastic rubber-like membranes

The present paper deals with the dynamic in ation of rubber-like membranes. The material is assumed to obey the hyperelastic Mooneyʹs model or the non-linear viscoelastic Christensenʹs model. The governing equations of free in ation are solved by a total Lagrangian nite element method for the spatial discretization and an explicit nite-di erence algorithm for the time-integration scheme. The numerical implementation of constitutive equations is highlighted and the special case of integral viscoelastic models is examined in detail. The external force consists in a gas ow rate, which is more realistic than a pressure time history. Then, an original method is used to calculate the pressure evolution inside the bubble depending on the deformation state. Our numerical procedure is illustrated through di erent examples and compared with both analytical and experimental results. These comparisons yield good agreement and show the ability of our approach to simulate both stable and unstable large strain in ations of rubber-like membranes