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Materials like paper, consisting of a network of natural fibres, exposed tovariations in moisture, undergo changes in geometrical and mechanicalproperties. This behaviour is particularly important for understanding thehygro-mechanical response of sheets of paper in applications like digitalprinting. A two-dimensional microstructural model of a fibrous network istherefore developed to upscale the hygro-expansion of individual fibres,through their interaction, to the resulting overall expansion of the network.The fibres are modelled with rectangular shapes and are assumed to be perfectlybonded where they overlap. For realistic networks the number of bonds is largeand the network is geometrically so complex that discretizing it byconventional, geometry-conforming, finite elements is cumbersome. Thecombination of a level-set and XFEM formalism enables the use of regular,structured grids in order to model the complex microstructural geometry. Inthis approach, the fibres are described implicitly by a level-set function. Inorder to represent the fibre boundaries in the fibrous network, an XFEMdiscretization is used together with a Heaviside enrichment function. Numericalresults demonstrate that the proposed approach successfully captures thehygro-expansive properties of the network with fewer degrees of freedomcompared to classical FEM, preserving desired accuracy.

Level set based eXtended finite element modelling of the response of fibrous networks under hygroscopic swelling