## 2 Methods
### Model for Contact Simulations  
To understand the three-dimensional contact behavior of the specimens during production, a simulation with a simple contact model is carried out. The model enhances the understanding of the complex interaction of the topography of the surfaces. The model is not used to predict the contact area of sintered green parts because there is no model available that accounts for the complex contact mechanics during the sintering process. The contact model is instead based on a Boussinesq approach [35]. The surface topographies used in the simulation are created with surface measurements from real, unsintered specimens. The specimens were measured with the mobile confocal microscope MarSurf CM mobile from the manufacturer NanoFocus AG, which is also used in this study to measure surface roughness. Two different specimens were measured: the upwards- and sidewards-facing surfaces (compare Section 2.5). From these initial measurements, equal sized cutouts were used as simulation topographies. Figure 7 shows an overview of two the topographies, the left topography is from the upwards-facing specimen and the right topography is from the sidewards-facing specimen. The surfaces of the topographies are shown from the top view. The topography of the upwards-facing surface is relatively smooth (see colorbar and scale of \(z\)-axis) and individual powder particles are visible. The topography of the  
Figure 6: Specim geometry used for experiments (dimensions in mm). sidewards-facing surface is rougher, and the individual, horizontally directed print layers are visible. For this model, the material is treated as homogeneous and solid. To account for the complex material behavior of the green part, the material parameters are modified and plastic deformation is introduced into the model so that the normal stress is limited. While this does not represent the complex contact mechanical behavior of the composite material or the nonlinear material behavior during sintering, it helps to understand the influence of the surface roughness and structure on the contact ratio and on the material deformation. The model gives insights into the contact geometry before sintering. In the simulation, the material is modelled with two parameters--the Youngs Modulus and the elasticity limit. The former represents the elastic resistance against deformation and the latter represents the maximum pressure for the elastic deformation. Any further pressure will lead to plastic deformation. The simple contact model of this simulation assumes that the load-carrying ability is limited to this elasticity limit, after which the cell will continuously plastically deform. The parameters were derived from the experiments and were set to 3 \(\times\) 10\({}^{9}\) Pa for the Youngs Modulus and to 2 \(\times\) 10\({}^{6}\) Pa for the elasticity limit. The domain was discretized with 251 \(\times\) 251 points. During the simulation, an iterative Newton algorithm is used to find the balance between gap height and applied normal stress. A starting gap height (with its correlated penetration) is chosen and the resulting normal stress is calculated. If the stress thus calculated is lower than the target stress, the gap height is decreased and vice versa. Simple plastic deformation is modelled by limiting the normal stress that an individual contact cell can transmit. The contact cell experiences further plastic deformation, but does not transmit more stress than the threshold. The results show that a significant amount of cells are plastically deformed (and thus transmit the maximum normal stress). For the brittle green parts, this is a reasonable behavior, however the behavior is directly influenced by the initial set of parameters. Figure 8 shows an overview of the surfaces before the start of the simulation. Two different cutouts from the same measurements are used for the upper and the lower topography.