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

摘要

The present paper deals with the dynamic inflation of rubber-like membranes. The material is assumed to obey the hyperelastic Mooney's model or the non-linear viscoelastic Christensen's model. The governing equations of free inflation are solved by a total Lagrangian finite element method for the spatial discretization and an explicit finite-difference 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 flow 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 different 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 inflations of rubber-like membranes.