## 2 Methods: Experiment and Numerical Simulation
### Numerical Models
#### 2.2.3 Interlaminar Damage Model  
In the paper, the delamination between interlayer interfaces or SMA and layer interfaces are modeled by surface-based cohesive behavior in Abaqus/Explicit. The surface-based cohesive behavior is defined as a surface interaction property, and can be used to model the delamination at interfaces directly in terms of traction versus separation [25; 26; 27; 28; 29]. The available traction-separation model in Abaqus assumes initially linear elastic behavior, followed by the initiation and evolution of damage. The elastic behavior is written in terms of an elastic constitutive matrix that relates the normal and shear stresses to the normal and shear separations across the interface. The elastic behavior can then be written as:  
\[\mathbf{t}=\left\{ \begin{array}{c}t_{n}\\ t_{s}\\ t_{\tau}\end{array} \right\}=\left[ \begin{array}{ccc}K_{tm}&0&0\\ 0&K_{ss}&0\\ 0&0&K_{tt}\end{array} \right]\left\{ \begin{array}{c}\delta_{n}\\ \delta_{s}\\ \delta_{t}\end{array} \right\}=\mathbf{K}\delta \tag{11}\]  
where nominal traction stress vector \(\mathbf{t}\) consists of three components--\(t_{n}\), \(t_{s}\) and \(t_{t}\)--which represent the normal and two shear tractions, respectively. Here, we adopt the uncoupled traction-separation behavior, and the terms \(K_{nn}\), \(K_{ss}\), and \(K_{tt}\) are not defined any dependencies on temperature or field variables. Abaqus uses default contact penalties to model the traction-separation behavior. Damage modeling simulates the degradation and eventual failure of the bond between two cohesive surfaces. The failure mechanism consists of two ingredients: a damage initiation criterion and a damage evolution law. The initial response is assumed to be linear, and once a damage initiation criterion is met, damage can occur according to a user-defined damage evolution law. Figure 3 shows a typical traction-separation response with a failure mechanism. Damage initiation refers to the beginning of degradation of the cohesive response at a contact point. The process of degradation begins when the contact stresses satisfy certain damage initiation criteria. Damage is assumed to initiate when a quadratic interaction function involving the contact stress ratios reaches a value of one. This criterion can be represented as: \begin{table}
\begin{tabular}{c c} \hline
**Mechanical Constants (Symbols)** & **Values** \\ \hline Young’s modulus (\(E_{1},E_{2},E_{3}\)) & 55.2 GPa, 18.4 GPa, 18.4 GPa \\ Poisson’s ratio (\(\
u_{12}\), \(\
u_{13}\), \(\
u_{23}\)) & 0.269, 0.269, 0.428 \\ Shear modulus (\(G_{12},G_{13},G_{23}\)) & 13.8 GPa, 13.8 GPa, 13.8 GPa \\ Ultimate tensile stress (\(X_{T},Y_{T},Z_{T}\)) & 1656 MPa, 73.8 MPa, 73.8 MPa \\ Ultimate compressive stress (\(X_{C},Y_{C},Z_{C}\)) & 1656 MPa, 91.8 MPa, 91.8 MPa \\ Ultimate shear stress (\(S_{12},S_{13},S_{23}\)) & 117.6 MPa, 117.6 MPa \\ \hline \end{tabular}
\end{table} 
Table 3: The material parameters of composites used in finite element (FE) simulation. Figure 3: Typical traction–separation response. \[\left\{\frac{t_{n}}{t_{n}^{0}}\right\}^{2}+\left\{\frac{t_{s}}{t_{s}^{0}}\right\}^ {2}+\left\{\frac{t_{t}}{t_{t}^{0}}\right\}^{2}=1 \tag{12}\]  
where, \(t_{n}^{0}\), \(t_{s}^{0}\), and \(t_{t}^{0}\) represent the peak values of the contact stress when the separation is either purely normal to the interface or purely in the first or the second shear direction, respectively. The damage evolution law describes the rate at which the cohesive stiffness is degraded once the corresponding initiation criterion is reached. Damage evolution can be defined based on the energy that is dissipated as a result of the damage process, which is also called the fracture energy.