Deployment analysis of membranes with creases using a nonlinear torsion spring model

Membranes have been widely applied in spacecrafts, such as solar sails and deployable antenna structures, due to their light weight and high compact ratio. The geometric profile of deployed membranes has an important impact on the performance of a membrane-based spacecraft, which should be accurately predicted during the deployment process. However, some observable dynamic deployment characteristics of membranes are difficult to be simulated accurately. In this paper, an equivalent torsion spring model for the membrane crease is proposed and derived to accurately describe the complex deployment process of the membrane. The elastic and plastic phases of the equivalent spring are both considered and derived in this model. Based on this method, the experimentally-observed spring-back position and the corresponding torque of the membrane can be quantitatively predicted. Combining the equivalent torsion spring model with the finite element software, the deployment processes of a single-fold and a Miura-fold are simulated and compared with the experimental results, showing a good agreement. Finally, the deployment process of a 3-axis stabilized solar sail is simulated using this method.