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The curl of thin freely dried paper sheets

FROM:
August Brandberg (1,2), Hamid Reza Motamedian (1,2), Artem Kulachenko (1,2) and Ulrich Hirn (2,3)
(1) Solid Mechanics, Department of Engineering Mechanics, KTH Royal Institute of Technology, Teknikringen 8D, 114 28 Stockholm, Sweden
(2) CD Laboratory for Fiber Swelling and Paper Performance, Graz University of Technology, Inffeldgasse 23, 8010 Graz, Austria
(3) Institute of Paper, Pulp and Fibre Technology, Graz University of Technology, Inffeldgasse 23, 8010 Graz, Austria

“The role of the fiber and the bond in the hygroexpansion and curl of thin freely dried paper sheets”, International Journal of Solids and Structures, Vol. 193-194, pp 302-313, 1 June 2020, https://doi.org/10.1016/j.ijsolstr.2020.02.033

ABSTRACT: A computationally efficient method to study the in-plane and out-of-plane dimensional instability of thin paper sheets under the influence of moisture changes is presented. The method explicitly resolves the bonded and the free segments of fibers in the sheet, capturing the effect of anisotropic hygroexpansion at the fiber level. The method is verified against a volumetric model. The importance of longitudinal fiber hygroexpansion is demonstrated in spite of the absolute value of longitudinal hygroexpansion being an order of magnitude lower than the transverse hygroexpansion component. Finally, the method is used to demonstrate the formation of macroscopic sheet curl due to a moisture gradient in structurally uniform sheets in the absence of viscoelastic or plastic constitutive behavior and through-thickness residual stress profiles.

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