Bridging network properties to the effective hygro-expansivity of paper: experiments and modelling

Dimensional stability issues may occur in paper sheets when subjected to moisture content variations. Paper is in fact mainly composed of hydrophilic wood fibres that experience significant dimensional changes upon humidity variations. The hygro-expansive deformations at the single fibre level and their effects on the meso-structural fibrous network govern the hygro-mechanical response of paper at the macroscopic, sheet scale. The present contribution aims at offering a relation between theoretical predictions and experimental measurements of the hygro-expansive behaviour of paper. Experimental observations of the hygroscopic and mechanical response at the sheet level have been performed, providing the anisotropic hygro-elastic properties of the material in the in-plane principal directions. To understand the multi-scale nature of the phenomenon, a periodic two dimensional meso-structural model of the fibrous network has been developed. The effective material response is extracted via homogenization. The influence of several meso-scale parameters (hygro-mechanical properties and geometry of fibres, inter-fibre bonds and of the network) on the overall behaviour of the material can be studied; in particular, the in-plane fibre orientation distribution along a preferential direction affects strongly the anisotropy of the macro-scale response. The proposed model has been adopted to represent the effective material response, focusing on the hygro-elastic response only and thus neglecting possible irreversible effects occurring at the different scales. A comparison of the experimental data with the results obtained from the model as a function of the fibre orientation distribution reveals a good accuracy of the prediction, thereby showing its applicability to estimate paper’s hygro-expansive response.