NC State
I. Kajanto. Finite element analysis of paper cockling. In Products of Papermaking, Trans. of the Xth Fund. Res. Symp. Oxford, 1993, (C.F. Baker, ed.), pp 237–262, FRC, Manchester, 2018.


A cockled paper sheet has lost its planarity because small (5 – 50 mm) randomly spaced areas have bent out of the plane of the paper. The variation in surface height is usually only of the order of one millimeter. Cockling is related to the hygroexpansivity and small-scale inhomogeneity of paper, and is a problem mainly with some lightweight papers and with copying papers.

In this study, cockling is analysed theoretically using the finite element method. The results suggest that cockling is caused by local inhomogeneity in the two-sidedness of paper. Small-scale variation in the fiber orientation angle is especially detrimental in this respect. Large variations in in-plane contraction can also cause paper to buckle. The intensity of cockling increases with decreasing paper thickness. The cockles become more oval as the fibre orientation gets stronger.

The conclusions of the theoretical analysis are supported by experiment. With high basis weight papers, the local fibre orientation of the top side was found to be almost independent of that of the bottom side. Thus, two-sidedness varies considerably on the small length scale, and this allows local curling to take place. At low basis weights the top and bottom sides are no longer independent, which offsets the amplifying effect of smaller thickness.

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