**2.5 Software validation of particle–wall collision**

In this paper, the ABAQUS software is used to simulate the particle–wall collision process, and it is compared with the numerical results by using the DEFEM. The ABAQUS is a finite element software applied to engineering simulation, which can simulate the stress and strain of large structures. This paper simulates the collision process between a spherical particle and the wall using the ABAQUS. The particle with a diameter of 0.05 m vertically hit the wall at a velocity of 0.5 m/s. The elastic modulus of the particles is 0.02 GPa, and the Poisson's ratio is 0.3. The elastic modulus of the wall is 2 GPa, and the Poisson's ratio is 0.3. After the contact force of particles is counted, the simulation results of ABAQUS and DEFEM are compared, as shown in **Figure 3**(**a**). It can be observed that the changing trend of the two results is the same, and the numerical value is similar. The contact force of the two numerical methods is re-zero near 0.003 seconds. In addition, the displacement of particles during collision and rebound is tracked, as shown in **Figure 3**(**b**). The results obtained by the two methods are in good agreement. It can be seen from these two results that the simulation results of the DEFEM are consistent with those of the ABAQUS.

*DEFEM Method and Its Application in Pebble Flows DOI: http://dx.doi.org/10.5772/intechopen.109347*

**Figure 2.** *Schematic diagram of the simulation process of the DEFEM.*

**Figure 3.**

*(a) Comparison of the results of DEFEM and ABAQUS software for contact force of the particle; (b) comparison of DEFEM and ABAQUS software for the displacement of the particle.*

Compared with the DEM, one of the advantages of the DEFEM is to calculate the dynamic deformation displacement and stress distribution of particles. It shows the comparison of deformation displacement calculated using the ABAQUS and the DEFEM, as shown in **Figure 4**. It can be observed that the distribution of the two methods is similar. The black vector in **Figure 4**(**b**) represents the deformation displacement at the grid node of the particle. Due to the collision between particles and the wall, the deformation near the wall is greater than that away from the wall, which also conforms to the relevant physical law.

#### **Figure 4.**

*(a) Static deformation displacement distribution calculated by ABAQUS software; (b) dynamic deformation displacement distribution calculated by the DEFEM (black vector represents the deformation displacement of nodes).*

**Figure 5.**

As shown in **Figure 5**, the static stress distribution of the particle calculated using the ABAQUS software has the same variation trend as the dynamic stress distribution calculated by the DEFEM, but there are some differences in values. Because the FEM is used to solve the problem in the ABAQUS software, it is considered that the contact force between particles only exists at the contact point. As shown in **Figure 5**(**b**), face contact is selected in the DEFEM. The multiple EDEs cover the boundary of particles. Therefore, the contact between particles can be transformed into the contact between EDEs, involving multiple nodes. The judgment and simulation process of the contact force are different between the two methods, so the stress distribution calculated by the two methods is different, but these differences are acceptable within the allowable error range.

Through the comparison between the ABAQUS software and the DEFEM, it can be observed that the DEFEM can well track the contact force, stress distribution, and movement in the process of particle collision, which also proves the accuracy of the DEFEM.
