Moisture-induced buckling of paper sheets, analysis and simulation

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Understanding the effects of water absorption on the geometry of a paper sheet is important for inkjet printing applications, since internal moisture content differences may cause unacceptable out-of-plane deformations. The present work focuses on moisture-induced deformations due to a moisture content that is uniform over the thickness of the sheet. Large enough in-plane differences will cause the sheet to buckle, leading to a wavy pattern at the edges of the sheet. Two approaches are utilized to study this for levels of moisture content up to and including the threshold for buckling. An analytical approach, based on geometrically nonlinear plate theory (von Kármán theory), and a numerical one, using commercially available finite element software, are presented. As a first reference problem an isotropic circular plate, wetted uniformly at its center, is solved both analytically and numerically for the in-plane stress distribution, the buckling threshold, and the resulting buckling mode. Secondly, the same is done for an orthotropic rectangular plate, wetted at its edges. Here, in the analytical approach a Rayleigh-Ritz analysis is employed to approximate the buckling threshold. The latter is also calculated by numerical means. The results show that the methods provide results consistent with each other.

LanguageEnglish
Pages296-308
Number of pages13
JournalInternational Journal of Solids and Structures
Volume128
DOIs
StatePublished - 2017

Fingerprint

Moisture
buckling
Buckling
moisture
Moisture Content
moisture content
thresholds
Simulation
simulation
Inkjet Printing
plate theory
circular plates
rectangular plates
plane stress
Circular Plate
Plate Theory
Plane Stress
Rectangular Plate
causes
Water absorption

Keywords

  • Buckling
  • Nonlinear simulation
  • Paper deformation
  • Rayleigh-Ritz method
  • Von Kármán plate theory

Cite this

@article{c0f8a7a304c14139a7cb97f56a7923cc,
title = "Moisture-induced buckling of paper sheets, analysis and simulation",
abstract = "Understanding the effects of water absorption on the geometry of a paper sheet is important for inkjet printing applications, since internal moisture content differences may cause unacceptable out-of-plane deformations. The present work focuses on moisture-induced deformations due to a moisture content that is uniform over the thickness of the sheet. Large enough in-plane differences will cause the sheet to buckle, leading to a wavy pattern at the edges of the sheet. Two approaches are utilized to study this for levels of moisture content up to and including the threshold for buckling. An analytical approach, based on geometrically nonlinear plate theory (von K{\'a}rm{\'a}n theory), and a numerical one, using commercially available finite element software, are presented. As a first reference problem an isotropic circular plate, wetted uniformly at its center, is solved both analytically and numerically for the in-plane stress distribution, the buckling threshold, and the resulting buckling mode. Secondly, the same is done for an orthotropic rectangular plate, wetted at its edges. Here, in the analytical approach a Rayleigh-Ritz analysis is employed to approximate the buckling threshold. The latter is also calculated by numerical means. The results show that the methods provide results consistent with each other.",
keywords = "Buckling, Nonlinear simulation, Paper deformation, Rayleigh-Ritz method, Von K{\'a}rm{\'a}n plate theory",
author = "{de B{\"o}ck}, R. and {van de Ven}, A.A.F. and L.H. Saes and J.M.L. Maubach and B. Koren",
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Moisture-induced buckling of paper sheets, analysis and simulation. / de Böck, R.; van de Ven, A.A.F.; Saes, L.H.; Maubach, J.M.L.; Koren, B.

In: International Journal of Solids and Structures, Vol. 128, 2017, p. 296-308.

Research output: Contribution to journalArticleAcademicpeer-review

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