Theory
Fracture Mechanics
Concrete is a composite material composed of coarse aggregate bonded together with a fluid cement which hardens over time, which is composed of atoms with the state of minimal energy. Once the certain stress of tension becomes similar to the crossing of the pass of energy, the cleavage forms (separation).
The materials including concrete contain a multitude of intern cracks as an ellipse (2b and 2c for small and large axes respectively). The concentration of stress produced by these defects is characterized by a coefficient of concentration of stress.
Finite Element Methods
As for modeling, the Finite Element Methods are utilized to simulate the ballistic collision and the resulting results of the objects. As Finite Element Method using a mesh does not enable to simulate high deformation, the meshless methods would be used to resolve this problem. The meshless methods enable to eliminate the mesh and perform the approximation from the nodes thus removing the geometric stresses. At each node, a weight function and a shape function are associated with a small domain. Among several meshless methods, the Element Free Galerkin Method(EFGM) would be used in this study. The EFGM enables large element distortion and creation of new surfaces for fracture mechanics.