KINEMATIC MODELING OF FINITE AXISYMMETRIC INFLATION FOR AN ARBITRARY POLYMERIC MEMBRANE OF REVOLUTION

The present paper studies the axisymmetric inflation of an enclosed polymeric membrane of revolution subject to quasi-static delivery of a fluid at required 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 conditions for the deformation field. With the use of the material's constitutive laws, these equations are converted to a two-point boundary value problem comprising a set of the first-order ordinary differential equations. The Newton-Raphson iterative algorithm, together with the fourth-order Runge-Kutta algorithm, is then utilized to develop relevant numerical schemes for kinematic simulation of membrane inflation. A geometric approximation on the first deformed membrane configuration is presented to start the solution procedure. In an attempt to obtain numerical convergent behavior along the equilibrium path of inflation, a displacement control strategy is suggested to mimic the quasistatic volume-controlled inflation process. Numerical simulations are carried out. The effects of different material models on the process of inflation are theoretically evaluated.