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

TL;DR

This paper introduces a level set and XFEM-based modeling approach to simulate the hygro-expansive response of fibrous networks like paper, efficiently capturing complex geometries and interactions with fewer computational resources.

Contribution

The paper develops a novel level set and XFEM framework for modeling hygro-expansion in fibrous networks, overcoming geometric complexity challenges of traditional finite element methods.

Findings

Successfully captures hygro-expansive properties of fibrous networks

Uses fewer degrees of freedom than classical FEM

Maintains accuracy in complex microstructural modeling

Abstract

Materials like paper, consisting of a network of natural fibres, exposed to variations in moisture, undergo changes in geometrical and mechanical properties. This behaviour 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 fibres, through their interaction, to the resulting overall expansion of the network. The fibres are modelled 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 fibres are described implicitly by a level-set function. In order to represent the fibre 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.