## 2 Materials and Methods  
### Finite Element Modeling (FEM)  
In this study, a drop impact test was employed in order to identify Bruise-related calculations associated with pear fruit. Extending our previous work [25], the Bruise susceptibility of pear fruit was studied experimentally by freely dropping a steel impactor into the pear fruit at three different height levels: 20 cm, 40 cm, and 60 cm. The schematic experimental setup is shown in Figure 2. The _Pyrus communis_ pear variety \"D'Anjou\" was selected for this study. A total of 129 pear samples were selected according to their uniform color, shape, and surface condition. Each pear sample weighed an average of \(163.12\pm 4.26\) g. In our previous work, we investigated the influence of pear fruit drop impact on Bruise volume, Bruise susceptibility, color, and firmness during a 14-day storage period. Color measurements were taken six times per sample, with an average of 104 readings per day. On the other hand, the firmness was checked every 2 days at intervals throughout the experiment. In this work, we replicated the experiment with the use of a finite element analysis tool in order to verify the results and validate the finite element (FE) model.  
The pear fruit was modeled using the SolidWorks 2023 SP 2.1 3D computer-aided design software. The 3D model of the pear fruit, along with its dimensions and properties, are shown in Figure 3a. The drop impact test of a steel ball impactor of 110 g mass was modeled in ANSYS 2022 R2 Workbench version 22.2.0. Fresh produce and agricultural products exhibit non-linear viscoelastic behavior. In this study, the elastic-plastic material model was adopted for the pear, where permanent plastic deformation can be simulated [12]. The material properties associated with each material used in this study are listed in Table 1 The FE model, along with the boundary conditions, are presented in Figure 3b. The steel ball was set to drop at a predetermined height, taking into consideration the standard earth gravity effect. Furthermore, the pear fruit was fixed from the bottom surface on the contact area with the floor.  
Figure 1: Flowchart of the proposed study.  
Figure 3: (**a**) 3D model and dimensions of the pear fruit. (**b**) FE model and boundary conditions.  
Figure 2: Physical experimental setup by [PERSON] et al. [25].  
Figure 3: (**a**) 3D model and dimensions of the pear fruit. (**b**) FE model and boundary conditions.  
To obtain the Bruise volume through FEA, the stress nodes that exceed the bio yield stress (0.3 MPa for pear fruit [12]) indicate the occurrence of bruising at maximum stress during collision. The sum of bruises in these nodes was used to obtain bruise volume and bruise susceptibility. The percentage of bruising is the ratio of bruised nodes to overall nodes. We can obtain the bruised mass by multiplying the bruising percentage by the known mass of the fruit. Bruise susceptibility (BS) is obtained through the following equation: BV is the bruise volume, and E is the internal energy of the pear fruit. BS values are typically very small values, as reported in the literature (9.56 \(\times\) 10\({}^{-6}\), 1.59 \(\times\) 10\({}^{-5}\), 1.62 \(\times\) 10\({}^{-5}\)) [12]. However, any small change in BS values has a significant impact on fruit shelf-life.  
\[\text{BS}=\frac{\text{BV}}{E}\ (\text{m}^{3}\text{J}^{-1}) \tag{1}\]  
In order to calculate the resulted energy from drop impact (\(E\)), the following equation was used as follows:  
\[E=m\ \times\ g\ \times\ \text{h}\ (\text{J}) \tag{2}\]  
where \(m\) represents the mass of the steel ball impactor in kilograms, \(g\) is the gravitational force (\(g=9.81\ \text{m}/\text{s}^{2}\)), and h is the predetermined drop height in meters.