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Bacterial cellulose is a biological macromolecule synthesized by bacteria of high purity and crystallinity. Bacterial cellulose nanofibers (BCNF) have been produced by soft homogenization and added to a recycled pulp to improve its quality. The benefits of BCNF on mechanical, physical and optical paper properties have been quantified and the retention mechanism of the BCNF in the paper network has been proposed. The use of BC to improve paper strength is usually limited by the decrease of tear index. The novelty of this work is that these two effects are decoupled by the addition of BCNF of low fibrillation (35.2%). In this way, some BCNF clusters are produced together with the individual nanofibers. Thus, with the addition of 3% BCNF, tensile and tear indexes as well as strain at break were improved by 11.1, 7.6, and 66.8%, respectively. Furthermore, the clusters were retained in the fiber network not only by hydrogen bonding, but also by physical retention within the gaps. Therefore, the addition of BCNF not only increases the mechanical properties of paper but also makes the handsheets more flexible and facilitates filler retention.

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. Denna doktorsavhandling behandlar modellering av tredimensionella fiber-nätverk med finita element metoden. Dels studeras numeriska aspekter av modelleringen, framförallt formuleringen av kontakten mellan fibrer, och dels tillämpningar av de utvecklade metoderna på fundamentala frågor som effekten av spridning i fiberegenskaper, inverkan av finmaterial och hygroexpansion. I den metod som används i avhandlingen representeras fibrer av balkelement och fogen mellan fibrer modelleras med hjälp av en punktvis balk-till-balk kontakt. Kontakt mellan balkelement är en särskild typ av kontaktproblem som introducerades av Wriggers och Zavarise 1997 för normal kontakt [1] och sedan utvidgades av Zavarise och Wriggers till att inkludera även tangentiell kontakt samt kontakt med friktionsvillkor [2]. Dessa formuleringar bygger på omfattande härledningar som resulterar i en konsistent tangentstyvhetsmatris. I avhandlingen visas att den numeriska implementeringen av den konsistenta formuleringen inte är tillräckligt robust för att användas vid slumpmässigt deponerade fibernätverk som innehåller ett stort antal kontakter. I de två första artiklarna i avhandlingen presenteras en enklare, icke- konsistent, formulering som visar sig ha ett mer stabilt konvergensbeteende för ett stort antal lastfall. Utöver detta är formuleringen lika exakt som den konsistenta formuleringen. Den första artikeln behandlar formuleringen av normal och tangentiell kontakt och den andra artikeln innehåller två formuleringar med både konsistenta och icke-konsistenta linjäriserade formuleringar för rotationskontakt mellan balkar i ett plan. Vi använde de utvecklade formuleringarna för att studera fundamentala problem inom fibernätverk som inte kan lösas med rent experimentella metoder. I den tredje artikeln undersöks effekten av variationer i fiber- och fogstyrka på dragstyvhet och nätverksstyrka och slutsatsen kan dras att för skeva fogstyrkefördelningar leder användandet av medelvärden för fibrers och fogars styrkeegenskaper istället för hela fördelningen inte till en representativ beskrivning av nätverket. I den fjärde artikeln undersöks mekanismerna bakom förbättringar i styvhet och styrka efter PFI-malning, vilket är en vanlig metod för att studera effekterna av malning på laboratorieskala. Genom användning av en kombination av experimentella och numeriska metoder fanns att en ökning i densitet, som ofta beskrivs som en av de huvudsakliga anledningarna bakom förbättringar av de mekaniska egenskaper efter PFI-malning, inte ensamt kan förklara de förändringar som observeras experimentellt. Slutsatsen är därför att den återstående delen av förbättringen orsakas av finmaterial, särskilt sådant som inte kan upptäckas med hjälp av moderna automatiska fiberkaraktäriseringsverktyg på grund av dessas begränsade upplösning. Slutligen, i den femte artikeln, presenteras en flerskalig modell för att studera hygro- expansion och krympningsegenskaper hos papper. På grund av fibrernas anisotropi har spänningsöverföringen i fiberfogarna en dominerande inverkan på pappersegenskaper när det utsätts för fuktförändringar. Vi modellerade fogarna mellan fibrer med hjälp av punktkontakter, men i själva verket krävs en finit kontaktarea för att korrekt beskriva spänningsöverföringen mellan fibrerna. För att överkomma denna begränsning och samtidigt bevara fördelarna med att använda balkelement utvecklades en flerskalig modell. I denna modell beskrivs varje kontakt i nätverket explicit. Via den aktuella fiberkonfigurationen överförs information till kontaktmodellen och denna i sin tur återför de inelastiska töjningarna till nätverkssimuleringen. Effektiviteten i en sådan modell demonstreras genom jämförelser med en fullskalig kontinuummodell. Med hjälp av den flerskaliga modellen kunde befintliga experimentella observationer kompletteras med nya insikter tack vare den obegränsade tillgången till detaljer i nätverket i varje steg av deformationsanalysen. QC 20180219

In this paper a simplified network model for mechano-sorptive creep is presented, which is a further development of an earlier paper [Strömbro, J., Gudmundson, P., 2008. Mechano-sorptive creep under compressive loading – a micromechanical model. International Journal of Solids and Structures 45 (9), 2420–2450.]. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys a constitutive law that is non-linear. Fibre kinks are included in order to capture experimental observations of larger mechano-sorptive effects in compression than in tension. Moisture dependent material parameters and anisotropy in the fibre distribution have been introduced. Theoretical predictions based on the model are compared to experimental results for an anisotropic paper both under tensile and compressive loading at varying moisture content and it is found that the important features in the experiments are captured by the model. Different kinds of drying conditions have also been examined.

The creep of paper is accelerated by moisture cycling, an effect known as mechano-sorptive creep. It has also been observed that the mechano-sorptive effects are larger in compression than in tension. In this paper a simplified network model for mechano-sorptive creep is presented. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre–fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys constitutive laws that are non-linear in stress. Geometrical fibre effects are included in the model in order to capture experimental observations of the differences between paper loaded in tension and compression. Theoretical predictions based on the developed model are compared to experimental results for paper both under tensile and compressive loading at varying moisture content. The important features in the experiments are captured by the model, i.e. the creep is accelerated by the moisture cycling and the mechano-sorptive effects are larger in compression than in tension.

Predictive migration models for polymers are already so well established that the European Commission intends to allow the use of the models as one quality assurance tool in product safety assessment of plastic materials and articles for food contact. The inhomogeneity of fibre-based materials makes modelling difficult-thus, little research has been done in this area. The authors compare experiments on the diffusion of certain volatile compounds through laboratory kraft pulp sheets with computer simulations in which the fibre network structure is modelled explicitly. The major advantage of the present random walk simulation is that it gives an estimate of the effective diffusion constant for the fibre network. For most compounds, the agreement between the experiments and simulations is good. The experiments and simulations indicate that gas diffusion rate is very sensitive to sheet porosity.