Hygro-mechanical structure–property relations for paper sheets

Our objective is to establish models which allow one to predict the hygro-mechanical properties of paper sheets based on the properties of the underlying fibrous network. Asymptotic homogenisation is used to determine rigorous effective properties of random networks numerically. The trend predicted by these random networks is however captured quite reasonably by a much simpler analytical model which assumes a regular network of perpendicular fibres. The latter model is fully analytical and is thus a much more powerful tool for developing understanding and designing materials. Predictions made by it compare well with measured hygro-expansivities reported in the literature.