  This paper presents a multi-scale approach to predict the effective
hygro-mechanical behaviour of paper sheets based on the properties of the
underlying fibrous network. Despite the vast amount of literature on paper
hygro-expansion, the functional dependence of the effective material properties
on the micro-structural features remains yet unclear. In this work, a
micro-structural model of the paper fibrous network is first developed by
random deposition of the fibres within a planar region according to an
orientation probability density function. Asymptotic homogenization is used to
determine its effective properties numerically. Alternatively, two much more
idealized micro-structural models are considered, one based on a periodic
lattice structure with a regular network of perpendicular fibres and one based
on the Voigt average. Despite their simplicity, they reproduce representative
micro-structural features, such as the orientation anisotropy and network level
hygro-elastic properties. These alternative models can be solved analytically,
providing closed-form expressions that explicitly reveal the influence of the
individual micro-scale parameters on the effective hygro-mechanical response.
The trend predicted by the random network model is captured reasonably well by
the two idealized models. The resulting hygro-mechanical properties are finally
compared with experimental data reported in the literature, revealing an
adequate quantitative agreement.
