A FINITE-ELEMENT FORMULATION FOR FINITE STATIC AXISYMMETRICAL DEFORMATION OF HYPERELASTIC MEMBRANES

A simple finite element formulation is presented in this paper for finite static axisymmetric deformation of isotropic incompressible hyperelastic membranes. This finite element procedure is derived from a recently published finite deformation membrane theory, in which Lagrangian type equilibrium equations, expressed in terms of the Biot stresses, are employed along with constitutive equations relating the principal components of the Biot stress tenser and of the principal stretches. Through consistent linearization of the equilibrium equations, a closed-form expression is obtained for the tangent stiffness matrix. In order to obtain the complete equilibrium path, the Newton-Raphson incremental-iterative method with displacement control is utilized. Numerical results are presented for inflation of a circular hyperelastic membrane. Various hyperelastic materials are considered.