# Effect of Initial Granular Structure on the Evolution of Contact Force Chains
## 2 Materials and Methods
### Photoelastic Model Particles and Test Program  
#### 2.2.1 Photoelastic Model Particles  
The granular assembly used in this experiment was composed of cylindrical model particles. As shown in Figure 1, particles with a diameter of 20 mm and height of 15 mm were made using polycarbonate (PC), and particles with a diameter of 10 mm and height of 15 mm were made using polytetrafluoroethylene (PTFE). Photoelastic sheets (0.5 mm- and 1 mm-thick; PS-1D and PS-1C, Vishay Intertechnology, Inc., Malvern, PA, USA) were cut manually into circles with diameters of 18 mm and 8 mm, respectively, and attached to PC and PTFE model particles using Loctite(r) 401 flex gel (Henkel AG & Company, KGaA, Dusseldorf, Germany). The elastic modulus (\(E\)) and Poisson's ratio (\(v\)) of the photoelastic sheets were 2.5 GPa and 0.38, respectively, and the \(E\) and \(v\) of the PC and PTFE were 13.5 GPa and 2.25 GPa, and 0.35 and 0.42, respectively. Unfortunately, no photoelastic response was observed for the 20-mm diameter shape throughout the experiment. This may be because enough force to observe the photoelastic response was not transmitted to the bottom layer, which consisted of particles with 20-mm diameters, or perhaps the wrong photoelastic sheet was selected. In this study, only the structural effects of the particles with 20-mm diameters on the particles with 10-mm diameters in the upper part of the laminates could be found. Therefore, this study was limited by the fact that the force applied to the particles with 20-mm diameters (PC particles) could not be analyzed quantitatively. In order to confirm the suitability of the manufactured model particles, the color patterns of the photoelastic sheets were observed by repeatedly loading and unloading the PTFE model particles, to which photoelastic sheets are attached, up to 294 N. Since the color patterns showed consistency at the same loading level during the loading and unloading process, it was determined that the model particles were suitable for repeated use and for maintaining elasticity within the applied load level.  
In this study, the scalar component of force was measured using [PERSON]'s [PERSON] (2010) quantitative method, which is suitable for a reflective, photoelastic granular assembly. Instead of the conventional method, wherein the fringe order is calculated at the point of contact, using this approach, the force from the color intensity in the center of a particle is analyzed (Figure 2). Considering that the force distribution and color intensity within the forced-particle were not homogeneous, the coefficient between the applied force and the corresponding color change was determined by correlating the average contact forces transmitted through a particle with the descriptive statistics, i.e., means and standard deviations, of the RGB color intensity in the center of the particle. The raw image was digitally transformed into separate greyscale images of the red, green, and blue colors. Once a square central region of interest (ROI) inside the particle was digitally selected, the RGB color intensities of pixels belonging to the ROI were extracted. The means and standard deviations of each RGB color  
Figure 1: Cylindrical model particles with photoelastic sheets.  
intensities were plotted against the applied particle force. According to [PERSON] and [PERSON] [21], each RGB color intensity showed three-segmented linear relationships with the particle force, and the best linear regression results were obtained using the red color. The best empirical correlation of the force with a single particle for each RGB color intensity may then be applied to calculate the forces of the individual particles in the overall assembly. Finally, the spatial distribution of the contact force chain can be quantitatively evaluated for the entire granular assembly. A detailed explanation of this methodology is provided by [PERSON] and [PERSON] [21].