On axisymmetric deformations of nonlinear viscoelastic membranes

Abstract

In previous work it was shown that a class of axisymmetric viscoelastic membrane problems can be reduced to the numerical solution of a system of partial differential--Volterra integral equations. This general method has the disadvantage that a change in constitutive equation requires rederiva- tion of specific details of the governing system. In this paper, a re- vised method is presented in which a change in constitutive equation does not affect the details of the governing equations. All that is needed is a change in the subprogram for computing stress from the deformation history.The revised method is illustrated for the case of the inflation of a cir- cular membrane by lateral pressure, a rheological experimental configura- tion. The membrane material is assumed to be a fluid such as polyisobuty- lene. This is in contrast to the solid type models used in all earlier examples. For this purpose, a BKZ model is developed from various sources.