## 3 Development of a Two-Dimensional Finite Element Model of a Unit Load Segment
### Contact Modeling  
In order to model the contact properties of the unit load segment, the static friction coefficients between the different components were measured. The coefficient of friction was measured for each of the contacts identified (Figure 2). The frictional values for the corrugated fiberboard were measured before the was converted into boxes. All coefficient of friction values were obtained following the slide angle method from the industry standard TAPPI T-815 (2018). This test method was used to evaluate the specific material's properties and ignore any additional variations that might be present when boxes are fully converted. Figure 2 shows the location of the contacts for the horizontal, vertical and pallet frictions. Friction coefficients were measured for each of the identified contacts and the corresponding alignment of the fluting structures. Horizontal box to box contact was measured as the contact between both boards along the machine direction. Vertical contact was measured as cross direction for both specimens. The payload contact with the pallet was evaluated with the corrugated board aligned along the machine direction, given the direction of box movement along the X-axis. Table 3 shows the coefficients of friction for each contact interaction. Experimental measurements of the coefficients of friction were replicated 10 times for each contact, reducing the commonly occurring variability in frictional forces on natural materials. Figure 3 shows the experimental test setup for the determination of the coefficients of friction of each of the identified contact interactions. For simplicity, the friction corresponding to the horizontal contact between boxes will be referred to as horizontal friction, the vertical contact between boxes as vertical friction, and the contact between the pallet and the payload simply as pallet friction. All measurements were conducted under standard laboratory conditions (50% relative humidity \(\pm\) 2%; 23 \(\pm\) 1 \({}^{\circ}\)C). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Property** & **Location** & **Type/Value** \\ \hline Loading & Entire model & Gravitational Acceleration \(-\)9.81 m s\({}^{-2}\) along Y-axis \\ Boundary conditions & Rack beams (2) & Fixed (encastre) \\  & Board & Frictional contacts \\  & Boxes (9) & Frictional contacts \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Loading and boundary conditions used for the unit load segment model. All the components were assembled together to replicate the pallet analog supporting a unit load of stacked boxes and resting on aluminum rack beams. In order to establish boundary conditions for the model and assure proper loading of the parts, surfaces were generated so every contact region could be explicitly declared. Towards this goal, all of the frictional contacts were created in the initial step and propagated to the subsequent loading steps. Every contact interaction was defined with friction properties and with tangential behavior using the penalty friction formulation. The normal behavior for the frictional contacts was determined using a penalty function as the constraint enforcement method. This was done to allow for separation of the components after contact was established. Small sliding was permitted in the formulation of the model to represent the small relative motions expected between boxes and between the boxes and the pallet analog. Each contact interaction was defined as a surface-to-surface contact with a node-to-surface discretization method. The unit load with three columns and three layers included two frictional contact interactions for the pallet analog with the rack beams, three contacts between the top  
Figure 3: Test setup for the determination of the coefficient of friction of the materials studied following the test standard TAPPI T-815 [46].