Viscoelastic Winding Mechanics

The viscoelastic analysis of tape systems composed of rate-dependent materials is presented. Histories for winding, winding-pause, and winding-pause-unwinding are considered. The winding problem is reduced to determining the appropriate Green’s function by numerical solution of a Volterra integral equation of the second kind. This Green’s function and integral superposition permits the evaluation of the stress and displacement fields in the tape system for any winding history. Viscoelastic unwinding is treated by the superposition of two-states — one determined from the initial condition of the tape when unwinding begins and the second state given in terms of an arbitrary external pressure evaluated by solving an integral equation. Numerical results are presented for several histories and representative material properties.