Scale effects in the hygro-thermo-mechanical response of fibrous networks

The response of fibrous materials to complex mechanical, hygroscopic and thermal loadings is a relevant research question in many engineering fields. In the literature, the behaviour of fibrous networks is typically investigated by assuming uniform loading conditions at the micro-structural level and by developing homogenization schemes that provide structure-property relations. However, in a number of situations, for instance in paper media used in digital ink-jet printing applications, the length scale of the applied loading (in this case of the moisture distribution) may be comparable to the characteristic length scale of the micro-structure. Therefore, a homogenized description may not be adequate for capturing the response of the fibrous network, even in an average sense. Indeed, the response of the network may depend on the ratio between the typical length scale of the loading and that of the micro-structure. The goal of this paper is precisely to investigate the scale effect on the network response due to the application of hygroscopic (or thermal) loads, which may rapidly fluctuate over the micro-structure. To this aim, a two dimensional fibrous network model is exploited. This model properly represents several network level features, such as the fibre's hygro-elastic properties and geometry, orientation, areal coverage, etc. The model is subjected to different moisture profiles, ranging from slow to fast oscillations. This reveals a pronounced size effect in the network deformation: the faster the moisture fluctuation, the higher the network's average strain. By exploring the dependence of the size effect on different micro-structural parameters, it is shown that the size effect is strictly related to the accommodation of fibre swelling by the voided network regions, and that therefore it is governed by the average size of the voids.