A Hypoelastic Model for Computing the Stresses in Center-Wound Rolls of Magnetic Tape

A hypoelastic finite element model for the calculation of continuous internal stress and deformation distributions in wound rolls used in center winding is presented. The stress problem is formulated as an initial boundary value problem and its solution satisfies continuity of deformation as one rewinds more layers on the growing roll. Hypoelasticity is shown to be a natural way to account for the growing body nature of a magnetic tape during winding. Several cases are examined with constant and radial stress dependent radial elastic modulus. The agreement with Hakiel’s model and experimental data obtained through the sandwiched pull strip method is very good. The results for the static linear and nonlinear cases examined found to be weakly dependent on the winding speed. The present analysis is more versatile than previous models in simulating the growing nature of the tape pack and it can naturally be extended to include nonlinear time and history-dependent phenomena.