Beam-to-Beam Contact and Its Application to Micromechanical Simulation of Fiber Networks

Sammanfattning: This doctoral thesis covers the topic of modeling the three-dimensional fiber net- works with the finite element method. It contains the part addressing the numerical aspects of the modeling, namely, the contact formulation and application of the developed methods to the fundamental questions such as the effect of randomness in fiber properties and effect of fines and hygroexpansion.In the approached used in the work,  the fibers were meshed with beam elements  and the bond between fibers is modeled using point-wise beam-to-beam contact. Contact between beam elements is a specific category of contact problems, which  was introduced by Wriggers and Zavarise in 1997 for normal contact [1] and later extended by Zavarise and Wriggers to include tangential and frictional contact [2]. These formulations encompass a large number of derivations and provide the consistent tangent matrix. We showed, however, the resulting numerical implementations based on these consistent formulations are not sufficiently robust in modeling random fiber networks with a large number of contacts.  In the first papers, we proposed a simpler non-consistent formulation, which turned out to be superior in terms of convergence stability with respect to the load step size for a wide range of loading cases. Having these advantages, it remained equally accurate as the original formulation.  The first paper covered the formulation of normal and tangential contact, and the second paper contains two formulations with both the consistent and non-consistent linearizations for in-plane rotational contact of beams.We use the developed formulations to address fundamental problems within the area of fiber networks, which  cannot  be solved  purely  with  experimental  tools.  In  the third article, we investigated the effect of fiber and bond strength variations on the tensile stiffness and strength of fiber networks and concluded that in cases of skewed distribution, using mean values for fiber and bond properties instead of the distributions is not always adequate to assess the changes these properties have on the average mechanical characteristics of the entire network.In the fourth paper, the mechanisms behind the improvement of stiffness and strength after PFI refining in the papermaking process is investigated. The PFI refiner is very popular for studying the effect of refining in the lab scale. By using a combination of experimental and numerical tools, we found that density, which is often mentioned as  the main reason behind the improvement of mechanical properties after PFI re- fining, cannot solely explain the degree of the change observed experimentally. We concluded the remaining part of the improvement is caused by the fibrillar fines, in particular, by the fines that cannot be detected with modern automated fiber characterization tools due to the limited resolution of such tools.Finally, in the fifth paper, we suggested a multi-scale model to study hygroexpan- sion/shrinkage properties of paper. Due to the anisotropy of the fibers, the stress transfer at the bonded sites has a dominant role in the behavior of paper when exposed to moisture change. While we modeled the bonds between fibers using point-wise contact elements, such stress transfer requires a finite contact area. To solve this limitation and yet preserve the advantages for using beams for modeling fiber networks, we developed a concurrent multi-scale approach.  In this approach,  the bond model is resolved for every bond in the network, and the exchange between the network and bond model is maintained through the current configuration of the fibers being passed to the bond scale,  and the inelastic strains being transferred   back to the network scale. We demonstrated the effectiveness of such approach by comparing it with a full-scale continuum model.  Using this approach, we were able  to complete the existing experimental observation with key insights using the ad- vantage of having unlimited access to the details of the network at each stage of the deformation.