Kinematic modeling of finite axisymmetric inflation for an arbitrary polymeric membrane of revolution

The present paper studies the axisymmetric inflation of an enclosed polymer ic membrane of revolution subject to quasi-static delivery of a fluid at re quired pressure. The membrane is assumed to be isotropic, hyperelastic, and incompressible. The Lagrangian formalism is employed to derive the system of governing equations along with the geometric relations and boundary cond itions for the deformation field. With the use of the material's constituti ve laws, these equations are converted to a two-point boundary value proble m comprising a set of the first-order ordinary differential equations. The Newton-Raphson iterative algorithm, together with the fourth-order Runge-Ku tta algorithm, is then utilized to develop relevant numerical schemes for k inematic simulation of membrane inflation. A geometric approximation on the first deformed membrane configuration is presented to start the solution p rocedure. In an attempt to obtain numerical convergent behavior along the e quilibrium path of inflation, a displacement control strategy is suggested to mimic the quasistatic volume-controlled inflation process. Numerical sim ulations are carried out. The effects of different material models on the p rocess of inflation are theoretically evaluated.