A rate-dependent continuum model for rapid converting of paperboard
Robertsson, Kristofer LU ; Wallin, Mathias LU ; Borgqvist, Eric LU ; Ristinmaa, Matti LU
and Tryding, Johan
LU
(2021)
In Applied Mathematical Modelling
99.
p.497-513
- Abstract
A rate-dependent continuum model for paperboard is developed within a framework for finite strains and finite deformations. A multiplicative split of the deformation gradient into an elastic and an inelastic part is assumed. For the in-plane modes of deformation, viscoelasticity is introduced via a thermodynamically consistent generalization of the Maxwell formulation. The elastic transition between out-of-plane compression and out-of-plane tension is smooth, excluding the need for a switch function which is present in a number of existing paperboard models. The evolution of the inelastic part is modeled using two potential functions separating compression from shear and tension. To calibrate the material model, a set of experiments at... (More)
A rate-dependent continuum model for paperboard is developed within a framework for finite strains and finite deformations. A multiplicative split of the deformation gradient into an elastic and an inelastic part is assumed. For the in-plane modes of deformation, viscoelasticity is introduced via a thermodynamically consistent generalization of the Maxwell formulation. The elastic transition between out-of-plane compression and out-of-plane tension is smooth, excluding the need for a switch function which is present in a number of existing paperboard models. The evolution of the inelastic part is modeled using two potential functions separating compression from shear and tension. To calibrate the material model, a set of experiments at different loading rates have been performed on single ply paperboard together with creep and relaxation tests for in-plane uniaxial tension. The model is validated by simulating two loading cases related to package forming, line-folding followed by subsequent force-relaxation and line-creasing during different operating velocities in conjunction with a creep study.
(Less)
- author
- Robertsson, Kristofer
LU
; Wallin, Mathias
LU
; Borgqvist, Eric
LU
; Ristinmaa, Matti
LU
and Tryding, Johan
LU
- organization
- publishing date
- 2021-11
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Anisotropy, Creasing, Folding, Large strains, Paperboard, Rate-dependent
- in
- Applied Mathematical Modelling
- volume
- 99
- pages
- 17 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85111041011
- ISSN
- 0307-904X
- DOI
- 10.1016/j.apm.2021.07.005
- language
- English
- LU publication?
- yes
- additional info
- Funding Information: This work was performed within Treesearch and financially supported by Tetra Pak and the strategic innovation program BioInnovation (Vinnova Project Number 2017–05399), a joint collaboration between Vinnova, Formas and the Swedish Energy Agency. The computations was enabled by resources provided by the Swedish National Infrastructure for Computing (SNIC) at LUNARC partially funded by the Swedish Research Council through grant agreement no. 2018–05973. Publisher Copyright: © 2021 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
- id
- e91cfeb1-5f8c-4118-95d4-4243014f7cef
- date added to LUP
- 2021-10-04 15:53:36
- date last changed
- 2025-04-04 14:17:56
@article{e91cfeb1-5f8c-4118-95d4-4243014f7cef,
abstract = {{<p>A rate-dependent continuum model for paperboard is developed within a framework for finite strains and finite deformations. A multiplicative split of the deformation gradient into an elastic and an inelastic part is assumed. For the in-plane modes of deformation, viscoelasticity is introduced via a thermodynamically consistent generalization of the Maxwell formulation. The elastic transition between out-of-plane compression and out-of-plane tension is smooth, excluding the need for a switch function which is present in a number of existing paperboard models. The evolution of the inelastic part is modeled using two potential functions separating compression from shear and tension. To calibrate the material model, a set of experiments at different loading rates have been performed on single ply paperboard together with creep and relaxation tests for in-plane uniaxial tension. The model is validated by simulating two loading cases related to package forming, line-folding followed by subsequent force-relaxation and line-creasing during different operating velocities in conjunction with a creep study.</p>}},
author = {{Robertsson, Kristofer and Wallin, Mathias and Borgqvist, Eric and Ristinmaa, Matti and Tryding, Johan}},
issn = {{0307-904X}},
keywords = {{Anisotropy; Creasing; Folding; Large strains; Paperboard; Rate-dependent}},
language = {{eng}},
pages = {{497--513}},
publisher = {{Elsevier}},
series = {{Applied Mathematical Modelling}},
title = {{A rate-dependent continuum model for rapid converting of paperboard}},
url = {{http://dx.doi.org/10.1016/j.apm.2021.07.005}},
doi = {{10.1016/j.apm.2021.07.005}},
volume = {{99}},
year = {{2021}},
}