## 3 Computational Methods
### Hybrid and Coupled Numerical Methods  
The hybrid methods are developed to take advantage of and overcome the shortcoming of the individual methods. The numerical simulation of the high-speed projectile penetrating soil target event using the \"Finite Element Method-Smoothed Particle Hydrodynamic Method (FEM-SPH)\" coupled algorithm is proposed by [PERSON] et al. [PERSON] et al. (2018). They observed that the \"FEM-SPH algorithm\" not only overcomes the defect of smooth particle tensile instability, but also overcomes the problem of low computational efficiency of the finite element method and can naturally simulate large deformation problems such as super-high-speed projectile-soil collision. The accuracy of the coupled FEM-SPH method depends on the algorithm suitable to the numerical calculation of the dynamic numerical calculation. The DAFL and semi-empirical resistance function-based formulation is applied via Finite Element Code ABACUS by [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) to predict the projectile trajectory under different oblique and yaw angles in the soil medium. They found that the projectile's relative mass center location had a strong influence on the projectile's rotation control. [PERSON] et al. [PERSON] et al. (2018) developed the analytical method, which implements DAFL and semi-empirical resistance function in ABAQUS explicit solver, for predictions of projectile penetration and perforation. The solution of a dynamically expanding spherical cavity in a finite sphere of incompressible \"Mohr-Coulomb target material\" accounts for variations in target resistance acting on the projectile's top and bottom sides due to the free surface impact. The numerical predictions are in good agreement with the normal and oblique penetration/perforation. \"[PERSON] et al. [99; 100] investigated the penetration behavior of the STING penetrometer numerically through the use of finite element and finite difference approaches. Shear strength is derived from the numerical experiments using cone factors and by application of a strain-rate correction [100]\". A three-dimensional finite element investigation of penetration into targets consisted of concrete layer and its semi-infinite foundation is due to [PERSON] and [PERSON] [101]. They reached the conclusion that the penetration depth, the residual velocity, and the projectile deceleration amplitude increases with the projectile's initial velocity. \"Three-dimensional dynamic FEM and DEM simulations\" of behaviors of penetration into granular target is performed by [PERSON] et al. [102] considering the impact of cylindrical projectiles on randomly distributed identical spheres. They noticed that this highly densified area was created just before the projectile and began to spherically propagate at a much higher speed than that of the projectile leaving a fairly rare area. Mechanical impedance of projectile and the mechanical properties of target materials play a predominant role on dynamic penetration phenomena. [PERSON] et al. [103] simulates the dynamic behavior of partially saturated sand under low-velocity impact loading by the hybrid approach using discrete element method (DEM) and the finite element method (FEM). The influence of capillary forces on the dynamic behavior of sand under high-pressure loading conditions is integrated in the simulation based on the capillary bridge model [104]. Experiments are also performed to examine the effect of water saturation on the height and shape of sand piles after impact, and to validate simulations. The simulations obtained experimental patterns of ejecta and height of the sand pile. They found that increasing water saturation (between 10 and 30 per cent) had an impact on the height of the sand pile at a drop height due to an increase in the cohesion between the particles. Mechanics of projectile penetration requires proper modelling and specifying constitutive equations for complex target materials, for example the heterogenous material soil.