## 2 The Numerical Tool Development
### Simulation Model Structure  
A Marc model was built as a thermal-structural model. The model included the following:  
* A transient thermal component;
* A structural quasi-static component.  
The transient thermal component handles thermal elements such as temperature variation, specific heat, thermal conduction, and thermal convection.  
The structural quasi-static component handles structural components such as Young's Modulus, Shear Modulus, Poisson's Ratio, deformations, internal stresses, etc.  
Both components run together, and each iteration solves thermal and structural components. A key parameter is needed to connect the two model components. This key parameter is \(\alpha\) = the cure degree.  
The curing degree is computed in the thermal component based on [PERSON] and [PERSON]'s implementation as a time and temperature function and specific material data. In the structural component, the curing degree is the parameter that imposes the variation in the structural parameter mentioned above. Also, based on the Bogetti and Gillespie mathematical model, the structure's shrinkage is defined.  
To illustrate the workflow logic and the functional steps of the model, we defined a model architecture diagram presented in Figure 18. It can be observed in the model functional diagram that the central component in the numerical model structure is the degree of cure space field as a function of time. To replicate the real-world scenario, the material's mechanical properties depend on the resin's degree of cure. The data flow used to obtain this dependency is described in the steps below:  
1. For each value of the degree of cure between 0 and 1, the resin has specific values of mechanical properties;
2. The resin-impregnated fibers have mechanical properties that may be considered constant in the working temperature range;
3. Using the DIGIMAT 2019.1 software tool and applying the homogenization theory, equivalent orthotropic material properties were computed for a resin-impregnated rely at different degrees of cure.  
Figure 17: EPOXY resin property variation computation with DIGIMAT.  
Before the heat transfer analysis passes, the curing analysis was performed based on the estimated temperatures at the beginning and the end of the increment. The cure rate was then calculated according to the cure kinetics of the resin materials. Using the cure rate, the heat flux due to cure reaction heat generation was calculated and added to the heat transfer system of equations. Volumetric curing reaction heat flux was calculated according to the cure rate [33]:  
\[Q^{C}=\frac{d\alpha}{dt}(1-V_{f})\rho_{r}H_{r} \tag{19}\]  
where \(H_{r}\) is the resin cure reaction, \(\rho_{r}\) is the resin density, \(\alpha\) is the cure degree, and \(V_{f}\) is the fiber volume fraction.  
The governing matrix equation for the cure-thermal coupled analysis is expressed as follows [33]:  
\[C(T)T^{\prime}+K(T)T=Q+Q^{I}+Q^{F}+Q^{C} \tag{20}\]  
In Equation (20), **C(T)** and **K(T)** are the temperature-dependent heat capacity and thermal conductivity matrices, respectively; **T** is the nodal temperature vector; **T** is the time derivative of the temperature vector; **Q** is the external heat flux vector; **Q** is the heat flux vector due to plastic work; **Q** represents the heat generated due to friction; and **Q** is the heat generated due to curing. Figure 19 is a plot illustrating the FE model's thermal boundary conditions.  
Figure 19: (**a**) Modeling convection at the surface of the coupon–mold assembly. (**b**) Modeling thermal contact between coupon and mold.  
Figure 18: Model architecture diagram.