Hygro-mechanical properties of paper fibrous networks through asymptotic homogenization and comparison with idealized models

TL;DR

This study develops a multi-scale model to predict paper's hygro-mechanical properties from fibrous microstructure, compares idealized models, and validates predictions with experimental data.

Contribution

It introduces a novel multi-scale modeling approach combining asymptotic homogenization with idealized models for paper properties.

Findings

Random fibrous network model captures microstructural effects

Idealized models provide analytical expressions for properties

Predicted properties agree well with experimental data

Abstract

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.