## 2 Materials and Methods
### Hertz-Mindlin and Bonding Parameter Model  
Using Hertz-Mindlin with bonding as a contact model between particles, bonding bonds are generated between disconnected neighboring particles to limit the relative motion between particles. Under the action of external forces, the particle spheres produce normal and shear displacements, and the bonding bond is analyzed from the force point of view by the changes in bending moment, torque, tension, pressure, and shear causing the bond breakage, and the bonding bond is established in the discrete element by the parameters of normal stiffness, shear stiffness, normal critical stress, and shear critical stress, so the force required for bond breakage is adjusted by the changes in the values of the bonding parameters, as shown in Figure 2. The bond will be broken when the stress between adjacent particles reaches its maximum value. Therefore, this contact model is suitable for simulating problems such as the breaking and fracture of corn straw under external forces [26]. The bond parameters of the epidermis, inner flesh, and epidermis-internal flesh of corn straw are critical to the formation of the bond bonds between the particles in the corn straw model and determine the accuracy of the discrete element model of corn straw. If the stiffness value of the bonding parameter is less than the sum of external forces on the particles, it will cause the straw model to collapse. On the contrary, if the stiffness value of the bonding parameter is too large, the elastic deformation of the contact part between the particles exceeds the critical value of the bonding bond, causing the particle model to blow up. The main parameters of the inter\(-\)particle bonding bond when the Hertz-Mindlin with Bonding model is used in the study are normal stiffness Kn, shear stiffness Ks, normal critical stress \(\sigma\), and shear critical stress \(\gamma\). The above parameters cannot be obtained directly by experiment, according to the Hertz-Mindlin with Bonding model theory [27] and [PERSON]'s shear theory [28], as Equation (1) is shown. Combined with the mechanical compression and shear tests of different structures of corn straw in the  
Figure 1: Shape of corn straws. Figure 2: Interaction forces between Hertz-Mindlin particles. previous phase of this project group and the related analysis [29; 30], the range of values of different bonding parameters is calculated and shown in Table 1.  
\[\left\{ \begin{array}{c}K_{\rm n}=\frac{4}{3}\left(\frac{1-\varepsilon_{a}^{2}}{ E_{a}}+\frac{1-\varepsilon_{b}^{2}}{E_{b}}\right)^{-1}\left(\frac{r_{a}+r_{b}}{r_{a} r_{b}}\right)^{-\frac{1}{2}}\\ K_{\rm s}=\left(\frac{1}{2}\sim\frac{2}{3}\right)K_{\rm n}\\ \sigma=\frac{F}{\pi R^{2}}\\ \gamma=c+\sigma\tan\varphi\end{array} \right. \tag{1}\]  
where \(\varepsilon_{a}\), \(\varepsilon_{b}\) is the particle Poisson's ratio; \(E_{a}\), \(E_{b}\) is the modulus of elasticity of particles, MPa; \(r_{a}\), \(r_{b}\) is the particle radius, mm; \(F\) is the critical pressure, N; \(R\) is the compressed cotton radius, mm; \(C\) is the stem cohesion, MPa; and \(\varphi\) is the angle of internal friction (\({}^{\circ}\)). At the mature stage, corn straw show different degrees of lignification and fibrosis, and the mechanical properties of different structures are different. Discrete element models of epidermis and inner flesh are established by using the approximation method, as shown in Figure 3.  
The discrete element model of the epidermis and inner flesh is established by the particle substitution method, and the modeling process is shown in Figure 4, based on Solidworks, to establish the geometric model of the epidermis and inner flesh of corn  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bonding Parameters** & \begin{tabular}{c} **Epidermal** \\ **Granules\(-\)Epidermal** \\ **Granules** \\ \end{tabular}  & \begin{tabular}{c} **Core Granules\(-\)** \\ **Core Granules** \\ \end{tabular}  & \begin{tabular}{c} **Core Granules\(-\)** \\ **Epidermal Granules** \\ \end{tabular}  \\ \hline \multirow{4}{*}{\