### Abstract

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.

Original language | English |
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Pages (from-to) | 933-947 |

Journal | Computational Mechanics |

Volume | 40 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2007 |

MoE publication type | A1 Journal article-refereed |

### Keywords

- Axisymmetric
- Large deformation
- Paper roll
- Winding

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## Cite this

Ärölä, K., & Von Hertzen, R. (2007). Two-dimensional axisymmetric winding model for finite deformation.

*Computational Mechanics*,*40*(6), 933-947. https://doi.org/10.1007/s00466-006-0152-8