Mean-field approach to compression of thick porous fibre networks

We discuss a new mean-field theory to describe the compression behaviour of thick low-density fibre networks. The theory is based on the idea that in very large systems, the statistics of free segment lengths causes the stress-deformation behaviour to be quantitatively predictable. The theoretical ideas are supported by several different experimental characterisations. Firstly, we have carried out single-fibre buckling tests using hemp fibres, which indicate a maximum level of axial stress before deformation localization, after which the load-carrying ability of a fibre decays. Secondly, the stress-compression behaviour of over 130 different foam-formed lightweight fibre materials were measured. For kraft pulps with low fines content, the average stress compression behaviour closely follows the theoretical prediction as described in terms of a universal s-function. Moreover, the acoustic emission can be described by the same function until collective phenomena cause deviations from the predicted behaviour. Similar deviations at smaller compressive strains are seen with furnishes with high fines content or added nanocelluloses together with samples with large voids. The localized buckling deformations lead to rapid stress re-distributions and subsequent fibre displacements in a fibre network as shown with in-situ CCD imaging.