Analysis of wrinkled membrane structures using a Plane Stress projection procedure and the Dynamic Relaxation method

Deployable membrane structures such as inflatable stratospheric balloons are known to be sensitive to the occurrence of local instabilities such as wrinkles. The wrinkling phenomenon affects the working performances of the membrane and the occurrence of this phenomenon has to be controlled numerically in order to predict the best means of deployment during the inflation of aerospace balloons. To improve their performances and reliability during flight, the balloons also need to be sized appropriately without the stress field being disturbed by the wrinkles. These instabilities originate numerically from the membrane elements which have a negligible bending stiffness. Several wrinkling models have been presented in the literature in order to solve this problem. However, in most of these models an elastic law and the Green deformation approach have been used for this purpose.The new model called the PS-DPS model presented here for correcting the effects of wrinkles on membrane structures was implemented in the in-house finite element software Herezh++. A projection technique based on a Newton–Raphson method is used to control the stress plane and the in-plane contraction. Using the Almansi strain formulation, this model also accounts for the changes in membrane thickness liable to occur during simulations. The problems due to numerical instabilities are overcome by determining the equilibrium with the so-called Dynamic Relaxation method using kinetic damping procedures. Unlike other membrane models of literature, the PS-DPS model can be used with materials showing complex mechanical behaviour of all kinds. Several benchmark problems are analysed with the present wrinkling model and compared with results available in the literature, focusing first on an elastic law and then on a non-linear hyperelastic law. Lastly, the inflation of a square cushion test and that of a Zero Pressure Balloon are simulated with this non-linear law. The results obtained indicate that the PS-DPS model is valid and accurate to take into account the wrinkles in flexible structures with all these linear and non-linear behaviours.