Large axially symmetric stretching of a nonlinear viscoelastic membrane

Abstract

Two problems of large planar axisymmetric deformations of an annular membrane consisting of a nonlinear viscoelastic material are solved, one with prescribed deformation at the outer boundary and one with prescribed force. These problems serve as examples to illustrate the extension to a class of viscoelastic membrane problems of a formulation of the corresponding elastic membrane problem suggested by Yang [1], which is especially convenient for numerical solution. The formulation uses radial and circumferential stretch ratios as dependent variables, which in the present case are found by solving a system of first order nonlinear partial differential-integral equations. The numerical procedure is such that at each time step, the problem is equivalent to a system of first order nonlinear ordinary differential equations for the current stretch ratios. This system is then integrated by the same numerical procedure as in the corresponding elastic problem.