The response of paper to humidity variations is a complex, inherently multi-scale problem. The hygroscopic swelling of individual fibres and their interactions within the fibrous network govern the macroscopic, sheet-level response. At this scale, moisture induced instabilities and out-of-plane deformations may occur, which are critical for a number of industrial applications. This work specifically focuses on several aspects of this important issue. A macroscopic phenomenological hygro-mechanical model is first proposed, which aims at predicting moisture induced out-of-plane deformations in paper sheets. The constitutive model is based on the relation between these deformations and typical irreversible phenomena associated to the history of paper manufacturing, i.e. the release of dried-in strains. The model is used to describe bending induced by moisture gradients through the thickness of the sheet as well as buckling due to moisture variation in the presence of mechanical constraints. The results of the model show that the anisotropic sheet-level hygro-expansion has a strong influence on the instability phenomena. Moreover, a comparison with experiments provides adequate semi-quantitative estimates. An additional step is made towards the multi-scale understanding of paper hygro-mechanics. The fundamental physical mechanisms governing the macroscopic moisture induced response are investigated on the basis of the underlying fibrous network. To this aim, a meso-structural model is developed which consists of a network of fibres randomly positioned in a planar region according to an orientation probability density function. A series of network simulations reveals that upon moisture content variations the expansion of the inter-fibre bonding regions essentially drives the overall deformation. Particularly in the case of anisotropic fibre orientation, this explains the origin of the macro-scale anisotropic hygro-expansion, which is essential for the observed sheet-level instability phenomena.
- Fibrous network
- Out-of-plane bending