## 2 Materials and Methods
### Establishment of Material Simulation Models
#### 2.3.2 Contact Model Setup  
Given the presence of wheat straw particles with diameters below 9 mm in the material, cohesive interactions between particles were anticipated due to electrostatic and surface energy effects. To account for these agglomeration phenomena, the Hertz-Mindlin with JKR (Johnson-Kendall-Roberts) cohesion contact model was selected for DEM parameter calibration [19]. This model, rooted in Hertzian contact theory, explicitly incorporates cohesive forces, making it particularly suitable for simulating materials prone to particle bonding and clustering (Figure 7).  
In the JKR cohesion simplified framework, the normal elastic force effectively characterizes the viscoelastic behavior between particles. This force is governed by the normal overlap and surface energy, ensuring accurate representation of adhesion dynamics. The model's ability to balance elastic recovery and energy dissipation during particle collisions aligns with the observed agglomerative tendencies of fine wheat straw particles, thereby enhancing simulation fidelity for biomass systems with inherent cohesive properties.  
\[F_{JKR}=-4\sqrt{\pi\gamma E^{*}}\alpha^{2}+\frac{4E^{*}}{3R^{*}}\alpha^{3}, \tag{5}\]  
\[\delta=\frac{\alpha^{2}}{R^{*}}-\sqrt{\frac{4\pi\gamma\alpha}{E^{*}}}, \tag{6}\]  
Figure 6: Silage corn components and discrete element particle models.  
Figure 7: Schematic representation of the JKR cohesive contact model.  
\[\frac{1}{E^{*}}=\frac{1-U_{1}^{2}}{E_{1}}+\frac{1-U_{2}^{2}}{E_{2}}, \tag{7}\]  
\[\frac{1}{R^{*}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}, \tag{8}\]  
where  
\(\mathrm{F_{JKR}}\): JKR normal elastic force (N);  
\(\alpha\): Normal overlap between contacting particles (m);  
\(\delta\): Tangential overlap between contacting particles (m);  
\(\gamma\): Surface energy (J/m\({}^{2}\));  
E*: Effective elastic modulus (Pa);  
R*: Effective contact radius (m);  
\(\mathrm{E_{1}}\), \(\mathrm{E_{2}}\): Elastic modulus of contacting particles (Pa);  
\(\mathrm{U_{1}}\), \(\mathrm{U_{2}}\): Poisson's ratio of contacting particles (dimensionless);  
\(\mathrm{R_{1}}\), \(\mathrm{R_{2}}\): Contact radius between particles (m).  
When the surface energy \(\gamma\) = 0, the JKR normal elastic force reduces to the Hertz-Mindlin normal force, expressed as  
\[F_{JKR}=F_{Hertz}=\frac{4}{3}E^{*}\sqrt{R^{*}\delta^{3}}, \tag{9}\]  
Even when particles are not in direct contact, the JKR contact model accounts for attractive cohesive forces. The maximum normal (\(\alpha_{\mathrm{c}}\)) and tangential (\(\delta_{\mathrm{c}}\)) gaps for cohesive interactions between particles are defined as  
\[\alpha_{\mathrm{c}}=\left[\frac{9\tau_{\mathrm{Y}}R^{*2}}{2E^{*}}-\left(\frac {3}{4}-\frac{1}{\sqrt{2}}\right)\right]^{\frac{1}{3}}, \tag{10}\]  
\[\delta_{c}=\frac{\alpha_{\mathrm{c}}^{2}}{R^{*}}-\sqrt{\frac{4\pi\gamma\alpha_ {\mathrm{c}}}{E^{*}}}, \tag{11}\]  
where  
\(\alpha_{\mathrm{c}}\): Normal maximum gap between particles under non-zero cohesive forces (m);  
\(\delta_{\mathrm{c}}\): Tangential maximum gap between particles under non-zero cohesive forces (m).  
When particles are not in direct contact and their separation is less than \(\delta\mathrm{c}\), the JKR cohesive force reaches its maximum value, given by  
\[F_{\mathrm{pull-out}}=-\frac{3}{2}\pi\gamma R^{*}, \tag{12}\]