Two-dimensional axisymmetric winding model for finite deformation

A two-dimensional axisymmetric winding model for wound rolls of thin web is developed. The model accounts for radial and axial displacements and radial, circumferential, axial and shear stresses. The roll build-up is modeled as an incremental accretion process. The material behaviour of the roll is considered as hyperelastic, orthotropic and radially nonlinear. The numerical solution is developed using the finite element method and the total Lagrangian formulation. The model is applied to the winding of paper rolls. It is shown that centrifugal forces may considerably affect the resulting stress distributions. For nonzero Poisson's ratios significant edge effects in the roll stresses are found. In particular, high shear stresses and shear stress gradients are discovered in the vicinity of the core near the roll ends. A remarkable stress leveling phenomenon is found where the effect of a non-constant incoming web tension is evened out in the roll axial direction.