Nonlinear viscoelastic membranes

Abstract

The subject of nonlinear viscoelastic membranes is an important class of problems within nonlinear viscoelasticity that involves interesting and important applications, computational issues and applied mathematics. The viscoelastic materials discussed in this paper are described by nonlinear single integral constitutive equations. After presenting the general constitutive framework, two fundamental membrane problems are formulated: the inflation of a circular membrane and the extension and inflation of a circular tube. Both problems involve large axially symmetric deformations and lead to a system of nonlinear partial differential–Volterra integral equations. A numerical method of solution is presented that combines methods for solving nonlinear Volterra integral equations and nonlinear ordinary differential equations. Finally, some properties of the equations are discussed that are related to the possibility that there may exist a critical time when the solution develops multiple branches.