Level set-based extended finite element modeling of the response of fibrous networks under hygroscopic swelling

Materials like paper, consisting of a network of natural fibers, exposed to variations in moisture, undergo changes in geometrical and mechanical properties. This behavior is particularly important for understanding the hygro-mechanical response of sheets of paper in applications like digital printing. A two-dimensional microstructural model of a fibrous network is therefore developed to upscale the hygro-expansion of individual fibers, through their interaction, to the resulting overall expansion of the network. The fibers are modeled with rectangular shapes and are assumed to be perfectly bonded where they overlap. For realistic networks, the number of bonds is large, and the network is geometrically so complex that discretizing it by conventional, geometry-conforming, finite elements is cumbersome. The combination of a level-set and XFEM formalism enables the use of regular, structured grids in order to model the complex microstructural geometry. In this approach, the fibers are described implicitly by a level-set function. In order to represent the fiber boundaries in the fibrous network, an XFEM discretization is used together with a Heaviside enrichment function. Numerical results demonstrate that the proposed approach successfully captures the hygro-expansive properties of the network with fewer degrees-of-freedom compared to classical FEM, preserving desired accuracy.