On the computational homogenization of three-dimensional fibrous materials

Fibrous materials such as paper, nonwovens, textiles, nanocellulose based-biomaterials, polymer networks and composites are widely used versatile engineering materials. Deformations at the fiber network scale have direct role in their effective mechanical behavior. However, computational description of the deformations is a challenge due to their stochastic characteristics. In consideration to this issue, the current study presents a computational homogenization framework at the fiber network scale to investigate how the fiber properties affect the mechanical properties at material scale. Methodology is based on (I) geometrical, spatial and mechanical modelling of fibers and fiber-to-fiber interactions, (II) formation of fiber network solution domain, boundary nodes on the solution domain and control nodes of the domain bounding the solution domain. The boundary value problem is then defined at the fiber network scale and solved with the proposed framework using the Euclidean bipartite matching coupling the boundary nodes and the control nodes represented in the form of corner, edge and surface nodes. The computed results show that the framework is good at capturing the fibrous material characteristics at different scales and applicable to the solution domains generated with stochastic modelling or image-reconstruction methods resulting in non-conformal meshes with non-matching boundary node distributions.