# The Mesoscopic Numerical Simulation of GAP/CL20/AP Composite Solid Propellant Based on MPM and FEM
## 4 Simulation Results and Discussion
### Effect of Interface Parameters on Macromechanical Properties  
The study of different interface parameter models shows that the three related parameters \(K\), \(T_{c}\), \(\delta^{f}\) in the interface model have significant influence on the mechanical properties of the propellant. By changing the interface parameters, the changes in the nominal stress-strain relationship curve are as follows:  
As shown in Figure 9a, when the initial stiffness \(K\) decreased from 683 MPa\(\cdot\)mm\({}^{-1}\) to 383 MPa\(\cdot\)mm\({}^{-1}\), the initial elastic modulus \(E\) of the propellant decreased from 2.214966 MPa to 2.039941 MPa, which reduced to the previous 92.0981%. When the initial stiffness \(K\) increased from 683 MPa\(\cdot\)mm\({}^{-1}\) to 983 MPa\(\cdot\)mm\({}^{-1}\), the initial elastic modulus \(E\) of the propellant increased from 2.214966 MPa to 2.0966 MPa, which up to the previous 103.8132%. It can be seen that with the increase in initial stiffness \(K\), the elastic modulus \(E\) of propellant increases gradually, but the growth rate becomes slower and slower. However, the parameter \(K\) has little influence on the peak value of nominal stress. As mentioned above, the initial interface stiffness \(K\) mainly determines the slope of the linear rising section of the stress-strain curve, and the increase in the initial interface stiffness \(K\) makes the stress increase rapidly in the early stage.  
As shown in Figure 9b, when the maximum fracture stress \(T_{c}\) decreased from 1.113 MPa to 0.613 MPa, the maximum stress \(\sigma_{\text{max}}\) of the propellant decreased from 1.143782 MPa to 0.703362 MPa, which reduced to the previous 61.4944%. When the maximum fracture stress \(T_{c}\) increased from 1.113 MPa to 1.613 MPa, the maximum stress \(\sigma_{\text{max}}\) of the propellant increased from 1.143782 MPa to 1.485626 MPa, which up to the previous 129.8872%. It can be seen that with the increase in initial stiffness \(T_{c}\), the maximum stress \(\sigma_{\text{max}}\) of the propellant increases. As mentioned above, the maximum fracture stress \(T_{c}\) mainly affects the peak value of the stress and determines the basic trend of the stress-strain curve. With the increase in the maximum fracture stress \(T_{c}\), the stress value increases.  
Figure 8: Stress–strain curve of GAP/CL20/AP propellant.  
As shown in Figure 9c, when the interface failure displacement \(\delta^{f}\) decreased from 0.211 mm to 0.061 mm, the maximum stress \(\sigma_{\text{max}}\) of the propellant decreased from 1.143782 MPa to 0.913491 MPa, which reduced to the previous 79.8658%. When the interface failure displacement \(\delta^{f}\) increased from 0.211 mm to 0.361 mm, the maximum stress \(\sigma_{\text{max}}\) of the propellant increased from 1.143782 MPa to 1.1661 MPa, which up to the previous 101.9512%. It can be seen that the interface failure displacement \(\delta^{f}\) mainly affects the damage softening section of the stress-strain curve. In the damage softening stage, the greater the interface failure displacement \(\delta^{f}\), the slower the stress decreases with the strain. If the failure displacement is too small, even in the case of a small strain, the interfaces are destroyed and lose their bearing capacity, and the stress in the model drops sharply (as shown by the blue curve in Figure 9c).