Elasto-plastic approach for paper cockling phenomenon: On the importance of moisture gradient

P. Lipponen (Corresponding Author), T. Leppänen, Jarmo Kouko, J. Hämäläinen

Research output: Contribution to journalArticleScientificpeer-review

22 Citations (Scopus)


Cockling of paper is a common problem occurring in the production, storage and end-use of paper. It is usually induced by a moisture content change. In many cases, cockling is an irreversible phenomenon; i.e. the initial shape is not obtained although the initial moisture content is restored. This kind of moisture content change occurs in copying machines and in the printing process, for example. In this paper, we present a continuum mechanical model, which is used to study the irreversible cockling of paper. In the model, paper is treated as an orthotropic elasto-plastic material and the model takes into account the small-scale variation of fibre orientation. The model is used to show the importance of the through-thickness moisture gradient on the cockling phenomenon during a cyclic moisture content change. The results suggest that the moisture gradient is a crucial factor for the irreversible cockling.
Original languageEnglish
Pages (from-to)3596 - 3609
Number of pages14
JournalInternational Journal of Solids and Structures
Issue number11-12
Publication statusPublished - 2008
MoE publication typeA1 Journal article-refereed


  • elastoplasticity
  • finite element
  • finite element analysis
  • paper
  • non-homogenous material
  • cockling
  • moisture gradient

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