# Compression and Fungal Heat Production in Maize Bulk Considering Kernel Breakage
## 3 Results and Discussion  
### Creep Behavior  
Creep deformation analysis (i.e., creep) is considered a valuable method in the quality assessment of grain/food products [12]. The deformation of maize under vertical load (i.e., gravity or weight of machine) results in a reduction in void ratio and ultimately impacts the moisture content, temperature, and biochemical functions. The deformation curve of maize bulk is shown in Figure 5a. Kernel breakage and vertical pressure affected the vertical compression of maize. Compression deformations of WK\({}_{50}\) and HK\({}_{50}\) after compression were 3.73 and 6.04 cm when loading was 50 kPa, and compression deformations of WK\({}_{150}\) and HK\({}_{150}\) after compression were 6.15 and 9.72 cm when loading was 150 kPa. The vertical compression of maize bulk increased with time under constant load. The compression of WK was small under the same vertical pressure. The compression deformations of HK were 62% and 58% higher than those of WK at 50 kPa and 150 kPa, respectively. The reason is that the grain skeleton composed of WK was not easily compressed, whereas HK easily slid and filled the pores, resulting in large compression deformation. Figure 4: Inspection of APC. Figure 5: Creep behavior of maize bulk: (**a**) \(s\)–log (_t_) curve and (**b**) creep model. The \(s\)-log (\(t\)) curve follows a reversed \(s\)-shape, and the deformation mainly underwent three stages: (1) Instantaneous deformation: the deformation was mainly affected by the magnitude of the load. The compression deformation occurred almost at the moment of load application, and the kernels slipped along the contact surface due to shear stress overcoming the friction at the contact surface. The kernels filled the large pores between kernels; (2) rapid deformation: the curve in this stage is mainly a section near the inflection point; the kernels were compressed, the pores between the kernels were filled, the resistance of the kernels increased, and the deformation rate decreased; (3) steady-state creep: the pores between kernels were basically filled, the resistance of kernels was greater, and the creep curve tended to be flat, roughly parallel to the abscissa axis. Although \(s\)-log \(t\) can reflect the deformation trend of maize, it cannot clearly explain the internal characteristics and compression mechanism of grain, and it is not convenient to calculate the settlement of grain bulk in the process of long-term grain storage. To avoid this defect and consider the practicability of the model, a three-element model was used in this study, as seen in Figure 5b. The first region is represented by the Hooke spring unit, which shows the initiation of elastic deformation in a very short time frame, known as the instantaneous elastic deformation. The second region is represented by the Kelvin element, which indicates the retarded elastic deformation [14]. The Kelvin element is composed of Hooke spring and dashpot in parallel and can be expressed as  
\[\sigma=E_{1}\varepsilon+\eta_{1}\dot{\varepsilon} \tag{2}\]  
where \(\sigma\) is the applied stress (MPa); \(\varepsilon\) is the total strain (dimensionless); \(E_{1}\) is the deformation modulus of creep stage (MPa); \(\eta_{1}\) is the viscosity coefficient of Kelvin (MPa-h). When the pressure is applied to the model, the spring will not be compressed immediately, due to the dashpot, and deformation gradually develops. Hooke spring is connected to the Kelvin element in series, and the creep model can be expressed as  
\[\eta_{1}\dot{\varepsilon}+E_{1}\varepsilon=\frac{E_{0}+E_{1}}{E_{0}}\sigma+ \frac{\eta_{1}}{E_{0}}\dot{\sigma} \tag{3}\]  
\[\varepsilon=\frac{\sigma}{E_{0}}+\frac{\sigma}{E_{1}}\bigg{(}1-e^{-\frac{E_{ 1}}{\eta_{1}}t}\bigg{)} \tag{4}\]  
where \(E_{0}\) is the instantaneous elastic modulus (MPa); \(\varepsilon_{0}=\sigma/E_{0}\); \(t\) is the storage time (h). The creep model of Hooke spring and Kelvin model in series can accurately describe the creep behavior of maize bulk under uniaxial compression.