Nonlinear orthotropic viscoelastic winding model

Abstract

A realistic and adaptive viscoelastic model for prediction of transient wound roll stress distributions is presented. The web material is taken to be orthotropic with a nonlinear radial creep compliance dependent upon interlayer pressure. Viscoelastic behavior is represented by a generalized Maxwell model for creep written as a convolution integral. Numerical solutions to the resulting integral boundary value problem give both initial and transient stress distributions within the wound roll. The model is successfully compared to the exact solution for a simple case of isotropy as well as to published works on this topic. In contrasting the solutions, the advantages and adaptability of this nonlinear formulation will be readily seen.