Numerical studies of wrinkling phenomenon in inflatable hyperelastic membranes undergoing multiaxial loadings

Thin membranes subject to multiaxial loadings may exhibit wrinkling phenomena. Modelling this phenomenon can be interesting if one wants to understand the origin of wrinkling and optimise the design of the membrane in order to avoid such kind of defect. The work, presented here aims at predicting wrinkling phenomena in thin hyperelastic membranes undergoing large deformation due to multiaxial loadings -using a finite element modelling tool for 3-D configurations. The constitutive equations used for modelling the membrane behaviour are hyperelastic models (the neo-Hookean model, the Mooney-Rivlin one and a third one with a higher degree of non-linearity). They have been implemented in a finite element code developed in our laboratory FORGE2005®, which is based on a mixed pressure-velocity formulation. The software is then applied to the deformation of a hyperelastic spherical form undergoing internal pressure. We show that the ability of tetrahedral elements to correctly predict wrinkling phenomena strongly depends on the various numerical parameters used (load increment, pressure ratio, mesh size, number of elements ...)