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.
Brandberg, A., Motamedian, H. R., Kulachenko, A., & Hirn, U. (2020). 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, 193-194, 302-313. https://doi.org/10.1016/j.ijsolstr.2020.02.033