## 3 Damage Analysis
### Numerical Modeling  
In order to compensate for the limitation of the number of experiments, a fragment impact composite/metal connecting structure model based on LS-DYNA was established. In composite modeling, the * PART_COMPOSITE keyword is used to define the basic physical parameters such as the thickness of each layer of the composite carbon fiber laminate component, and the layup direction. In order to better reflect the loss between different layers independently in the modeling, and to take into account the computational scale and efficiency, a modeling scheme of one 2D shell cell layer is used instead of four to five actual layers, i.e., five 2D shell cell layers (i.e., elements in the meshing) are used in the simulation modeling instead of 25 actual layers of composite material for the bottom skin  
Figure 17: Top skin damage in Situation 2. Figure 18: Top skin damage in Situation 3.  
components, and five 2D shell unit layers are used instead of 22 actual layers of composite material for the stringent components. The * MAT_COMPOSITE_DAMAGE model is a composite constitutive model commonly used on shell units, containing physical quantities such as density, fiber elastic modulus in three directions, Poisson's ratio, shear modulus and longitudinal tensile strength, and transverse tensile strength, and can be used to define various orthogonal anisotropic materials with brittle fractures, which is applicable to the T300/QY8911 epoxy resin-based carbon fiber unidirectional laminate in this study. The single-layer carbon fiber laminate thickness direction size is much smaller than the other direction size. Hence, it can be analyzed according to the plane stress problem, considering only the in-plane stress state, ignoring the plane normal upward stress. The stress-strain relationship can be expressed as:  
\[[\sigma]=[S][\epsilon] \tag{1}\]  
\[\frac{1}{[S]}= \begin{bmatrix}\frac{1}{E_{11}}&\frac{\
u_{12}}{E_{11}}&\frac{- \
u_{31}}{E_{32}}\\ \frac{-\
u_{12}}{E_{12}}&\frac{-\
u_{22}}{E_{23}}&0\\ \frac{-\
u_{31}}{E_{33}}&\frac{-\
u_{23}}{E_{23}}&\frac{\
u_{3}}{E_{33}}\\ &0&0&\frac{1}{2C_{23}}&0\\ &0&0&\frac{1}{2C_{31}}\\ \end{bmatrix}  \tag{2}\]  
where \(\sigma\) is the stress, \(\epsilon\) is the strain, \(E\) is the elastic modulus, \(\gamma\) is the [PERSON]'s ratio, and \(G\) is the shear modulus. The * MAT_COMPOSITE_DAMAGE model uses the Chang-Chang failure criterion and has the following four failure modes:  
1. If \(\sigma_{an}>0\), fiber is in the stretched state, when satisfied: \[\left(\frac{\sigma_{aa}}{X_{T}}\right)^{2}+\beta\left(\frac{\sigma_{ab}}{S_{ c}}\right)-1\geq 0\] (3) Herein, \(E_{a}=E_{b}=\
u_{ba}=\
u_{ab}=G_{ab}=0\) and the fiber undergoes stretching failure;
2. If \(\sigma_{an}<0\), the fiber is in compression, when the following conditions are met: \[\left(\frac{\sigma_{aa}}{X_{C}}\right)^{2}-1\geq 0\] (4) Herein, \(E_{a}=\
u_{ba}=\
u_{ab}=0\) and the fiber fails in compression;
3. If \(\sigma_{bb}>0\), the fiber matrix is in a stretched state, when the following conditions are met: \[\left(\frac{\sigma_{aa}}{Y_{T}}\right)^{2}+\left(\frac{\sigma_{ab}}{S_{c}} \right)-1\geq 0\] (5) Herein, \(E_{a}=\
u_{ba}=G_{ab}=0\) and the fiber matrix undergoes a stretching failure;
4. If \(\sigma_{bb}<0\), the fiber matrix is in compression, when the following conditions are met: \[\left(\frac{\sigma_{bb}}{2S_{C}}\right)^{2}+\left[\left(\frac{Y_{C}}{2 Sc} \right)^{2}-1\right]\frac{\sigma_{bb}}{Y_{C}}+\left(\frac{\sigma_{ab}}{S_{C}} \right)^{2}-1\geq 0\] (6) Herein, \(E_{a}=\
u_{ba}=\
u_{ab}=G_{ab}=0\) and the fiber matrix fails in compression. The Johnson-Cook constitutive model, Mie-Gruneisen equation of state, and maximum tensile stress damage criterion were used for the Al alloy in the structure. The Johnson-Cook model [10] differs from the common plastic theory in that it characterizes the material response to impact and penetration through parameters such as processinghardening, deformation rate effects and thermal softening.