Fiber networks are ubiquitous due to their low cost and high ratio of mechanical performance to weight. Fiber networks made of cellulose fibers from trees are used as information carriers (paper) and as packaging (board). Often the ideal product is both mechanically sturdy and possible to print on. This thesis investigates the underlying reasons for the mechanical performance of paper and board through the discretization and direct simulation of every fiber in the network.

In Paper A the effect of fiber-fiber bond geometry on sheet stiffness is investigated. Many packaging products seek to maximize the bending stiffness by employing stiff outer layers and a bulkier layer in the middle. In bulky sheets, the fibers are frequently uncollapsed resulting in a more compliant bonded segment. Because all the loads in the network are transferred via the bonds, such compliance can cause unexpectedly large decreases in mechanical performance. Although many models have been presented which aim to predict the tensile stiffness of a sheet, these predictions tend to overestimate the resulting stiffness. One reason is that the bonds are generally considered rigid. By finite element simulations, we demonstrated the effect of the lumina configuration on the stiffness of the bonded segment on the scale of single fiber-to-fiber bonds, and that the average state of the fiber lumen has a marked effect on the macroscopic response of fiber networks when the network is bulky, has few bonds, or has a low grammage.

Compression strength is central in many industrial applications. In paper B we recreated the short span compression test in a simulation setting. The networks considered are fully three-dimensional and have a grammage of 80 to 400 gsm, which is the industrially relevant range. By modeling compression strength at the level of individual fibers and bonds, we showed that fiber level buckling or bifurcation phenomena are unlikely to appear at the loads at which the macroscopic sheet fails.

In paper C, we developed a micromechanical model to study the creation of curl in paper sheets subjected to a moisture gradient through the sheet. A moisture gradient is always created during the printing process, which may lead to out-of-plane dimensional instability. We showed that the swelling anisotropy of individual fibers bonded at non-parallel angles causes an additional contribution to the curl observed on the sheet level.

Fiber networks made of cellulose fibers from trees are used as information carriers (paper) and as packaging (paperboard). This thesis investigates the mechanical performance of paper and paperboard via micro-mechanical modeling and presents new methods for the mechanical characterization of the micro scale, necessary in such models.        In Paper A the effect of the fiber-fiber bond geometry on the sheet stiffness is investigated. In thick, low density sheets, the fiber lumen remains open resulting in a more compliant bonded segment. By finite element simulations, we demonstrate the effect of the lumen configuration on the stiffness of the bonded segment. Most important for the stiffness of the segment is the average state of the fiber lumen which has a marked effect on the macroscopic response of fiber networks when the network is sparse.        Compression strength is central in many industrial applications. In Paper B we recreated the short span compression test in a simulation setting. The networks considered are three-dimensional and have a grammage of 80--400 gm^-2. By modeling compression strength at the level of individual fibers and bonds, we show that widespread fiber level buckling is unlikely to appear at the loads at which the macroscopic sheet fails.        

In Paper C we develop a micro-mechanical model to study the creation of curl in paper sheets subjected to a moisture gradient through the thickness of a sheet. A moisture gradient is created during the printing process if the ink is water based, which may lead to  out-of-plane deformations (curl). The effect of transverse fiber shrinkage is captured using a multiscale model where the fiber-fiber bond is modeled with volume elements. We show how the swelling anisotropy of individual fibers contributes to the curl of the sheet in such settings. 

In Paper D we present how to uniquely and compactly describe the distribution of fiber shapes (length, width, wall thickness, curl) used in network simulations. Using a canonical vine structure, fiber shapes measured using an optical image analyzer are used to construct a multivariate distribution function. New fiber geometries can then be generated by sampling from this distribution. Having access to such a complete description with both the distribution of fiber properties and the dependence between properties is shown to be superior to previously presented methods using micro-mechanical simulations of thermo-mechanical (TMP) long fiber sheets.        In Paper E we compare sheet testing, micro-mechanical tensile testing, and nanoindentation as methods to extract the elastic material properties of individual pulp fibers. Nanoindentations are performed parallel to and orthogonal to the axis of the fiber after it has gone through all steps of papermaking, and indentation moduli are extracted. By relating the indentation modulus to the components of the anisotropic stiffness tensor, the longitudinal and transverse elastic modulus can be determined via an iterative error minimization scheme. We show that nanoindentation is an alternative to traditional methods with the advantage of yielding the transverse modulus and enabling measurement of the fiber properties after papermaking.