Journal
MECHANICS OF MATERIALS
Volume 108, Issue -, Pages 11-20Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.mechmat.2017.01.013
Keywords
Paper; Fibrous network; Multi-scale models; Asymptotic homogenization; Hygro-mechanical properties
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Funding
- Research Program of the Materials innovation institute M2i [M61.2.12458]
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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. (C) 2017 Elseviei Ltd. All rights reserved.
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