## 4 Numerical Simulation Applied to the FFF Process
### Material Property Characterization
Differential Scanning Calorimetry (DSC) is widely applied to identify thermal transitions, including glass transition temperature (Tg), melting point (Tm), and crystallinity, which affect shrinkage and stiffness, particularly in semicrystalline polymers like PLA and PA. Additionally, micro-computed tomography (micro-CT) allows the non-destructive, high-resolution imaging of internal porosity, fiber distribution, and interlayer adhesion. These structural insights support the validation of mesoscale simulations and help to relate internal features to mechanical behavior [64]. Material failure mechanisms have also been studied extensively. [PERSON] and [PERSON] (2017) [65] conducted FEA and experimental tests to study the effect of raster  
Figure 16: Load–displacement curves from CT tests. The numerical model response is compared to experimental results. (**a**) Classical samples printed with \(\pm 45^{\circ}\) raster orientation; (**b**) Optimized samples with filament aligned along the principal stress direction. Adapted from [62]. angle and layer thickness on tensile failure. They found that thinner layers improve elongation and load-bearing capacity due to the higher number of load-aligned layers, while thicker layers result in higher tensile strength because of fewer air voids and stronger interlayer bonds. Figure 17 illustrates the stress distribution across samples with different raster angles and layer thicknesses. Specimens with 0\({}^{\circ}\) rasters exhibit more uniform stress distribution along the loading direction, while those with 90\({}^{\circ}\) rasters show stress localized at the interlayer regions, leading to early delamination. In 0\({}^{\circ}\)/90\({}^{\circ}\) raster configurations, failure typically initiates in the 90\({}^{\circ}\) layers and propagates through the structure, ending in brittle fracture of the 0\({}^{\circ}\) layers. These results highlight the need for refined models that can better capture interlayer bonding behavior and failure progression in anisotropic printed parts. Expanding on anisotropy in AM, [PERSON] et al. (2025) [66] reviewed the mechanical behavior of additively manufactured materials, focusing on how the layer-by-layer process creates structural heterogeneity, residual stress, and defects. Their analysis found that materials, process parameters, and post-processing techniques all influence anisotropic behavior, with metals, polymers, and composites responding differently. Crystal plasticity models accurately predict anisotropy in metals, but polymer models often oversimplify microstructural effects. They emphasized the need for improved modeling approaches that integrate machine learning and multi-scale physics but noted that many current models lack validation across different AM processes, highlighting the need for better experimental benchmarking and real-time simulation improvements. To improve failure detection, [PERSON] et al. (2025) [12] developed a simulation-in-the-loop framework for real-time structural validation in AM. Their system combines FEA with in  
Figure 17: Cross-sectional stress distributions from FE simulations of FFF specimens with different layer thicknesses and raster angles, including a solid specimen. Adapted with permission from [65]. situ defect detection, using a U-net image segmentation model to analyze defects layer by layer. Experimental tests on a material extrusion printer demonstrated that the framework could predict failure strength within 5% accuracy, allowing for early defect detection and automated print termination when necessary. They found that defect size and distribution directly influence stress accumulation, but computational efficiency remains a challenge in complex geometries and high-speed printing. The progression of strain distribution in a defective sample under tensile loading is illustrated in Figure 18.  
To further enhance failure prediction and quality assurance in FFF, thermography-based approaches have also been explored. [PERSON] et al.