## 2 Material and Methods
### Finite Element Analysis Model  
A Finite Element Analysis (FEA) model is a numerical representation of a physical system that uses a mesh of discrete elements to approximate and solve complex engineering problems involving stress, strain, thermal, or other field variables under given boundary conditions and loads. It is necessary to emphasize the importance of acquiring precise material properties to analyze key characteristic parameters, their response, and the scale of localized stresses. Besides tensile stress and Young's modulus, the tangential modulus of elasticity plays a significant role in the numerical model parametrization. The tangent modulus is the slope of a line tangent to the flow curve featured at a plastic point of interest. Following recommendations from [37], the Ansys software (v.17.1) utilized a multilinear isotropic hardening material model. The FE model (Figure 8) is sandwiched between a moving flat surface (defined displacement load condition along negative Z) and a fixed flat surface (lower cut-off surface). Given the computational efficiency and significant deformation due to lower relative density, a large deflection was used in quasi-static testing. The reaction forces are measured in the upper lattice area and numerically linked with the displacement of the upper contact  
Figure 7: Experimental testing of the specimen and corresponding TrapeziumX Force-Displacement chart (Sst1-1: Red Curve; Sst1-2: Purple Curve; Sst1-3: Green Curve; Sst1-4: Blue Curve; Sst1-5: Yellow Curve). surface opposite the fixed flat surface. Analog to experimental testing results, charts, and the appearance of maximum forces, the displacement value along the negative Z axis was set at 1 mm of deformation (parameterized FE model). A parameterized FE model featuring a 50 \(\times\) 50 \(\times\) 50 tessellation was established using the standard mesh element discretization. Due to the low relative density of the structures, the numerical model considers large deflection in the parametrization setup. It implies that the stiffness is no longer a constant but varies as it progresses through the load path. Thus, tangential stiffness represents the tangent to the force-deflection curve at a particular point in the load path. Therefore, numerical parametrization involves the time stepping in loading conditions. This will force the parameterized FE model to apply the load in smaller steps. It calculates an optimum time step at the end of each substep based on the structure's response to the applied loads. The numerical model aims to iterate loading conditions until the residual becomes acceptably tiny and the solution is converged. Generally, the manufacturing process significantly influences the mechanical properties of additively manufactured lattice structures [38]. Although similar \"printing defects\" were expected to occur in all specimens, this study did not focus on including any of these imperfections. As a result, the modifications of the hardening model were not impacted by these defects. Therefore, the modified volumetric hardening model shown in reference [14] was not used to establish a numerical material model in this research. The intention of establishing a multilinear isotropic hardening model was to separate material definition into two independent effects of elastic and plastic behavior and, thus, achieve different temperature-dependent data sets where the elastic modulus significantly impacts that region and plastic strain-stress behavior after the yielding process begins. Concerning the accurate determination of the hardening model, stress versus plastic strain data points must be specified, starting from the yield stress of the prime material. This means that the starting point in the multilinear isotropic hardening model is the yield stress value, and the plastic strain is zero. These data serve in the numerical model for internal calculation of the tangent modulus for every two consecutive data points in the plastic region. Figure 8: Parameterized FE model with defined boundary conditions.