# The Mesoscopic Numerical Simulation of GAP/CL20/AP Composite Solid Propellant Based on MPM and FEM
## 5 Conclusions  
When the GAP/CL20/AP composite solid propellant was subjected to an external load, micro-cracks, micro-hole expansion, and local stress concentration may destroy the microstructure of interface bonding, thus affecting its macro-mechanical properties. Based on the advantages of the material point method and the finite element method, this paper systematically carried out a meso-damage experiment on the composite propel  
Figure 9: Effect of interface parameters on the stress–strain curve. (**a**) The stress–strain curves under different parameters \(K\); (**b**) the stress–strain curves under different parameters \(T_{c}\); (**c**) the stress–strain curves under different parameters \(\delta^{f}\). lant and a numerical simulation study of its mechanical behavior, mainly including the following contents:  
1. In this paper, the microstructure model of a GAP/CL20/AP composite solid propellant was established based on the MPM. The developed Fortran codes are suitable for generating grains with arbitrary shapes, such as CL20 and AP grains. The grains are generated in order from largest to smallest. The minimum distance between the generated grains can be controlled by adjusting the size of the background grid. The filling ratio of grains can meet the requirements of the grain proportion in a real propellant. In this paper, it takes about 15 min to generate grains in this numerical model. Therefore, it shows that the numerical model generated by this method is efficient. The generated AP and CL20 grains are imported into the commercial software Abaqus through python scripting codes for numerical calculation. 2. In this paper, a numerical simulation of the uniaxial tension of the meso-model was carried out using the commercial finite element software Abaqus. The evolution process of interface damage between CL20 grains and AP grains, and the GAP adhesive matrix thus becomes clear. Furthermore, the relationship between meso-damage and the macro-stress-strain curve is clearly expressed. During the initial stage of the uniaxial tensile nominal strain reaching 30%, the bonding interface between grain substrates is well bonded. The propellant is in the linear elastic region. As the nominal strain reaches 60%, debonding occurs first in the vicinity of large grains and dense grain areas, and the stress-strain curve begins to appear nonlinear. As the nominal strain reached 80%, a large number of interfacial debonding occurred, and the stress hardly increased with the increase in strain. It can be considered that the simulation results can reflect a real experiment. 3. 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. The initial interface stiffness \(K\) mainly determines the slope of the linear rising section of the stress-strain curve. The maximum fracture stress \(T_{c}\) mainly affects the peak value of the stress. The interface failure displacement \(\delta^{f}\) mainly affects the damage softening section of the stress-strain curve. According to the research above, it can be seen that the macroscopic mechanical properties of a GAP/CL20/AP propellant strongly depend on the evolution of its microstructure. However, the micro-numerical simulation of propellants is not perfect, such as the establishment of a three-dimensional micro-model. In the micro-finite element calculation, it is considered that the main factor of composite propellant damage is the debonding of the particle-matrix interface. In fact, the internal microstructure of composite propellants is very complicated during storage and transportation, and the interface damage is only one important factor. Other factors, such as damage and tear of the binder matrix, need to be fully considered in a follow-up study.