A Multi-Scale Approach for Finite Element Method Structural Analysis of Injection-Molded Parts of Short Fiber-Reinforced Polymer Composite Materials

Abstract

Short fiber-reinforced polymer composites are extensively used in automotive structural components, such as engine mounts and motor mount brackets, due to their favorable strength-to-weight ratio. For motor mount brackets, accurate structural analysis requires consideration of fiber orientation, as it significantly affects the mechanical behavior of the composite. This study aims to investigate the influence of fiber orientation heterogeneity on the mechanical properties of short fiber-reinforced polymer composites formed by injection molding. The spatial variation of the fiber orientation tensor, which evolves from the gate to the flow end during molding, presents challenges in experimental characterization. To address this, microscale analysis was conducted using injection-molded tensile specimens, followed by mesoscale modeling through representative volume elements (RVEs). Homogenization techniques were applied to predict effective mechanical properties, which were subsequently used to evaluate the performance of actual components at the macroscale. The findings demonstrate the importance of multi-scale modeling in capturing the anisotropic behavior of fiber-reinforced composites and provide a framework for more reliable structural analysis in automotive applications.

1. Introduction

Multi-scale modeling is a widely adopted approach in various scientific and engineering disciplines including physics, chemistry, materials science, and structural engineering to study systems or phenomena that span multiple spatial or temporal scales [1,2,3]. This approach is not only used to predict the mechanical properties of fiber-reinforced polymer (FRP) composites, such as those reinforced with glass or carbon fibers, but also to investigate failure mechanisms [4]. For example, J. Llorca proposed a bottom–up multi-scale modeling strategy that integrates material behavior from the nanoscale to the macroscale, enabling high-fidelity virtual mechanical testing of composite structures [5]. Eleftherios developed a multi-scale material model capable of capturing the coupled damage and healing behavior of epoxy matrices in composites by integrating nonlinear mean-field homogenization with continuum damage-healing mechanics [6].

The core concept of multi-scale modeling is to integrate information from nano- and microscale material structures into macroscopic models, thereby enabling a comprehensive understanding of system behavior. In materials science and structural engineering, this approach is particularly important for analyzing complex materials and structures, as it helps bridge the gap between microscopic features such as fiber orientation, fiber structure, and resin-to-fiber weight ratio and macroscopic properties like strength and elasticity.

Short fiber-reinforced plastic (SFRP) composites are typically manufactured via injection molding, where the fiber orientation and resin-to-fiber weight ratio significantly influence the mechanical properties [7]. In this context, H. Mehdipour developed a constitutive model that captures the nonlinear mechanical behavior of SFRPs, incorporating plasticity-induced deformation and post-yield damage through a non-local damage framework. This model, implemented in ABAQUS via a UMAT subroutine, effectively simulates the anisotropic and rate-dependent response of short fiber composites and has been validated against experimental tensile and compression data for PA6 with GF60 [8].

Analysis of fiber orientation in injection-molded SFRP composites reveals its sensitivity to shear rate. Near the surface, increased shear rate aligns fibers parallel to the flow direction, while in the core, reduced shear rate results in perpendicular or random orientations [9]. Micro-CT imaging of actual tensile specimens confirms that fiber orientation varies significantly from the surface to the core. These variations are reflected in the fiber orientation tensor, which differs across the cross-section due to the flow characteristics of the injection molding process.

This study also confirms that tensile specimens molded in different orientations such as flat molds versus standard tensile specimen molds exhibit different stress–strain behavior, highlighting the influence of fiber orientation on mechanical properties. Since fiber orientation strongly affects the anisotropic behavior of SFRP composites [10], multi-scale modeling is essential for accurate property prediction [11].

In the case of FRP composites, 3D printing technology has enabled the design of various fiber orientations, represented by fiber orientation tensors. Studies have shown that mechanical properties vary significantly depending on these tensors [12]. However, producing tensile specimens for every fiber orientation is impractical, making it difficult to evaluate material properties experimentally. As a result, structural simulations often rely on anisotropic properties derived from flat-molded specimens, using only the principal direction of the fiber orientation tensor for each mesh element. This simplification limits the accuracy of conventional finite element methods (FEMs) in predicting the behavior of SFRP composites [13].

To overcome these limitations, this study estimates effective material properties of SFRP composites using FFT-based homogenization methods [14,15,16,17,18]. PA66 with 50 (wt%) glass fiber (GF50) was selected as the representative material. Injection molding simulations were conducted to obtain fiber orientation tensors, which were then used to construct representative volume elements (RVEs) for each mesh in the FEM model. Microscale modeling was applied to incorporate both fiber orientation and resin-to-fiber weight ratios. Using homogenization, orthotropic properties were generated for each mesh element, reflecting the predominant fiber orientation.

The proposed multi-scale modeling approach was validated by comparing simulation results with experimental hammering test data for a key electric vehicle component: the motor mount bracket. The results confirmed that the model effectively captures fiber orientation and orthotropic mechanical behavior in injection-molded SFRP composites.

2. Materials and Methods

2.1. Materials

In this study, the selected material was polyamide 66 (PA66) reinforced with 50 wt% (32 vol%) glass fiber, a composite widely utilized in injection molding applications. PA66/GF50 (wt%) offers an excellent balance of mechanical strength, thermal stability, and processability, making it particularly suitable for structural components. Among fiber-reinforced thermoplastics, this formulation is one of the most commonly adopted in the automotive and industrial sectors due to its proven performance under demanding mechanical and thermal conditions [19].

The Zytel 101L NC010 (DuPont, Wilmington, DE, USA) used in this study is a lubricated polyamide 66 (PA66) resin specifically engineered for injection molding applications. E-glass fiber was selected as the reinforcing agent due to its high strength-to-weight ratio and cost efficiency, making it a standard choice in fiber-reinforced plastics. The fibers used in the composite had an average length of approximately 180 µm and a diameter of about 10 µm, which are representative of the fiber geometry typically observed in molded PA66 composites.

Table 1. Mechanical properties of PA66 and GF.

Material	Young’s Modulus E (GPa)	Poisson Ratio	Bulk Modulus K (GPa)	Shear Modulus G (GPa)
PA66	0.986	0.4	1.644	0.352
Glass fiber	72	0.22	42.857	29.508

presents the mechanical properties of PA66 and glass fiber, including Young’s modulus, Poisson’s ratio, bulk modulus, and shear modulus. The properties of PA66 were determined through experimental testing using tensile specimens supplied by the manufacturer, while those of the glass fiber were compiled from technical datasheets provided by the supplier.

Figure 1 illustrates the rheological and thermodynamic characteristics of PA66 reinforced with 50 wt% glass fiber: (a) viscosity as a function of shear rate, and (b) the isobaric pressure–volume–temperature (PVT) curve. Viscosity measurements were conducted in accordance with ASTM D3835 [20], while PVT data were obtained following ASTM D792 [21].

2.2. Specimen of Tensile Test Preparation and Testing Methods

Figure 2 depicts the preparation process for tensile test specimens. A flat plate was first produced via injection molding, after which specimens were precisely machined using CNC equipment to prevent processing-induced damage. Tensile specimens were extracted at orientations of 0° (parallel to the flow direction), 45°, and 90° relative to the injection flow.

Figure 3 shows the heating zones within the cylinder of the injection molding machine, configured according to the conditions listed in

Table 2. Injection molding process conditions.

Cylinder Head Temperature (°C)				Injection Molding Conditions
NH	H1	H2	H3	Pressure (%)	Time (s)
315	310	290	280	80	4
				Holding Pressure Conditions
				Pressure (%)	Time (s)
				30	10

. Table 2 details the molding parameters for the flat plate mold. NH (Nozzle Heating) indicates the nozzle temperature, while H1, H2, and H3 correspond to the temperatures of sequential zones within the cylinder, with H1 being closest to the nozzle. The molding conditions were optimized to minimize deformation of the molded plates. Injection molding was primarily controlled by time, with pressure and speed set as percentages of the equipment’s maximum capacity rather than absolute values. These settings—typically between 80% and 90%—were used to determine actual pressure and speed values, which were back-calculated based on the predefined injection time. Real-time monitoring of the molding behavior was performed using pressure gauges installed on the equipment. The same control strategy was applied in the process simulation, where injection time was fixed and holding pressure was defined as a percentage of the calculated injection pressure, ensuring consistency between experimental and simulated conditions.

A total of 20 flat plates were fabricated. Based on surface quality and dimensional consistency, 10 plates were selected for specimen preparation. From each selected plate, tensile specimens were machined at orientations of 0°, 45°, and 90° relative to the flow direction using CNC equipment to prevent processing damage. For each condition, five replicate tensile tests were conducted, and the average values were used for analysis.

To prepare dumbbell-shaped specimens for tensile testing, flat-shaped molds (180 × 180 × 4 mm) were used to produce specimens oriented at 0°, 45°, and 90° with respect to the injection flow direction. Figure 4 presents the geometry of the tensile specimens used in accordance with the ASTM D638M standard [22]. The dimensional specifications of the specimens are provided in

Table 3. Dimensions of the tensile specimen.

Specimen Dimension [mm]	b1	b2	h	L3	L	t	A
	9.86	19.82	3.92	172.64	115	3	38.65 mm2

, while the tensile test conditions are detailed separately in

Table 4. Tensile test conditions.

Temperature	26 °C
Humidity	43%
Speed	2.4 mm/min
Gauge Length	50 mm

. Figure 4a shows a photograph of the tensile specimen, and Figure 4b illustrates the schematic drawing of the specimen. For each orientation, five replicate tensile tests were conducted, and the average values were used for analysis.

2.3. Product Manufacturing and Testing Methods

Figure 5 illustrates the development and application of the motor mount bracket in an electric vehicle. Initially manufactured from aluminum, the bracket was redesigned using a short fiber-reinforced polymer composite to reduce overall vehicle weight. The final product was fabricated via injection molding and subsequently assembled with a rubber bush through a pressing process. The bracket is installed on the vehicle chassis to suppress noise and vibration from the cotter and must meet a strength requirement of 20 kN. The composite material used is identical to that employed in the tensile test specimens. Figure 6 presents the mechanical testing setup used to evaluate the tensile and compressive strength of the motor mount bracket. The left panel shows the actual test configuration, where tensile (blue arrow) and compressive (red arrow) loads are applied. The right panel provides a schematic diagram indicating the force application points and restraint conditions. To simulate operational loading, three-point restraints were applied to the vehicle structure, enabling accurate assessment of the bracket’s performance under both tension and compression.

Figure 7 depicts the hammering test method used to measure dynamic stiffness. The left panel shows the experimental setup with axes labeled X, Y, and Z, representing the directions of impact. Sensors were installed at designated response points (marked as “1”) to capture vibrational data during hammer excitation. The right panel illustrates the schematic of the clamped-free condition, highlighting the hammering directions and sensor locations. This method enables multi-directional dynamic characterization of the bracket under realistic boundary conditions.

2.4. Fiber Structure Analysis and Generating Mechanical Properties Method

2.4.1. Fiber Orientation Tensor Method and RVE Modeling Method

Jeffery proposed a theoretical model for the rotational motion of ellipsoidal particles in a viscous fluid [23], which has become a fundamental theory in theoretical studies of fiber orientation. To date, the Folar–Tucher model has been the best available description for short-fiber-orientation representation in concentrated suspensions [24,25,26].

To obtain fiber orientation tensor results, SIGMAsoft was used, and fiber orientation tensor of each element of the mesh model for structural analysis was reviewed and reflected in RVE modeling.

To perform RVE modeling (as shown in Figure 8), 3D micro-XRM imaging was conducted on both the surface and core layers of the injection-molded tensile specimens. The resulting images were analyzed using the FiberFind AI module in GeoDict to extract quantitative data, including fiber orientation tensors (XX, YY, ZZ), volume fractions, lengths, and diameters. Figure 8 presents a structured table dividing each region into four sub-layers, with specific orientation and volume fraction values. Additionally, graphical plots of fiber length and diameter distributions were added to improve the interpretability of the microstructural data.

As part of the microstructural characterization, Figure 8a,b present 3D micro-CT images of the tensile specimen taken at the mid-length position, with a resolution of 1 μm. The specimen, with a total thickness of 3.92 mm, was divided into a 1 mm core layer and a 1 mm surface layer for analysis.

Table 5. Fiber orientation tensors and fiber volume fraction of central layer and surface layer.

Fiber Orientation Components by Layer (vol.%)		Fiber Orientation			Vf (%)
		X-Axis (%)	Y-Axis (%)	Z-Axis (%)
Micro-CT analysis (Core layer)	1st Layer	63.0477	17.6956	19.2567	31.8003
	2nd Layer	66.1844	18.2655	15.5502	31.9499
	3rd Layer	70.9015	15.0393	14.0592	32.2798
	4th Layer	76.1767	11.3675	12.4558	32.0796
Micro-CT analysis (Surface layer)	1st Layer	81.4451	7.7954	10.7565	32.7301
	2nd Layer	79.8369	7.9518	12.2113	32.4027
	3rd Layer	80.0405	7.8215	12.1378	32.3877
	4th Layer	81.2374	7.4823	11.2802	32.7593

shows the results of fiber orientation tensor and fiber volume fraction analysis, conducted using the FiberFind AI module of the GeoDict2024 software based on the 3D micro-CT data. The specimen thickness was segmented into eight layers from the core to the surface, and average values were calculated for each layer.

The analysis reveals that fiber alignment in the flow direction (X-axis) increases toward the surface. Specifically, the average fiber orientation in the core region is approximately 65%, while in the surface region it increases to around 81%, indicating a clear gradient in orientation across the thickness.

Figure 8c illustrates the distribution of fiber length and diameter within the composite. The average fiber length and diameter were approximately 180 µm and 10 µm, respectively, representing the typical fiber geometry observed in the molded material. These geometric characteristics, previously described in the Section 2, were utilized in the RVE modeling process. An average fiber volume fraction of 32% was applied. During the RVE modeling, the fiber orientation ratios for both the flat plate and engine mount components were obtained using the fiber orientation tensor results from the SIGMAsoft Virtual Molding 6.1.1 software.

2.4.2. Mechanical Properties Method

By averaging the strain in the structure, it is impossible to obtain the Hooke’s law for the general anisotropic case.

$${\sigma }_{ij}={\sum }_{r,s=1}^3{c}_{ijrs}{ϵ}_{rs} i,j \in \{1,2,3\}$$

(1)

Here, the tensor c is a symmetric fourth-order tensor and is referred to as the elasticity tensor. Typically, the elasticity tensor, stresses, and strains are written in Voigt notation. In this method, the elasticity tensor takes the form of a 6 × 6 matrix, and the stresses and strains can be expressed as 6 × 1 vectors.

In

Table 6. Index assignment.

Tensor notationindex(ij)	11	22	33	23, 32	31, 13	12, 21
Voigt notationindex	xx	yy	zz	yz	zx	xy
	1	2	3	4	5	6

, symbols for representing the stresses of each component are organized. Subscripts x, y, and z signify the geometric x-axis, y-axis, and z-axis, respectively. The stress tensor σ_ij and the strain ε_ij can be expressed in Voigt notation.

$$\sigma =\left(\begin{array}{c}{\sigma }_{11}\\ {\sigma }_{22}\\ {\sigma }_{33}\\ {\sigma }_{23}\\ {\sigma }_{31}\\ {\sigma }_{12}\end{array}\right) \epsilon =\left(\begin{array}{c}{\epsilon }_{11}\\ {\epsilon }_{22}\\ {\epsilon }_{33}\\ {\epsilon }_{23}\\ {\epsilon }_{31}\\ {\epsilon }_{12}\end{array}\right)$$

(2)

Accordingly, Hooke’s law can be expressed as a matrix vector product.

$$\left(\begin{array}{c}{\sigma }_{11}\\ {\sigma }_{22}\\ {\sigma }_{33}\\ {\sigma }_{23}\\ {\sigma }_{31}\\ {\sigma }_{12}\end{array}\right)=\left(\begin{array}{c}{c}_{11}\\ c_{12}\\ c_{13}\\ c_{14}\\ c_{15}\\ c_{15}\end{array}\begin{array}{c}{c}_{12}\\ c_{22}\\ c_{23}\\ c_{24}\\ c_{25}\\ c_{26}\end{array}\begin{array}{c}{c}_{13}\\ c_{23}\\ c_{33}\\ c_{34}\\ c_{35}\\ c_{36}\end{array}\begin{array}{c}{c}_{14}\\ c_{24}\\ c_{34}\\ c_{44}\\ c_{45}\\ c_{46}\end{array}\begin{array}{c}{c}_{15}\\ c_{25}\\ c_{35}\\ c_{45}\\ c_{55}\\ c_{56}\end{array}\begin{array}{c}{c}_{16}\\ c_{26}\\ c_{36}\\ c_{46}\\ c_{56}\\ c_{66}\end{array}\right)\left(\begin{array}{c}{\epsilon }_{11}\\ {\epsilon }_{22}\\ {\epsilon }_{33}\\ {\epsilon }_{23}\\ {\epsilon }_{31}\\ {\epsilon }_{12}\end{array}\right)$$

(3)

This is the stress–strain relationship of an anisotropic material where there is no symmetry between the material properties.

Considering SFRP composite materials as orthotropic materials, if the properties are symmetric with respect to each symmetrical plane for E₁, E₂ and E₃, the general form of the stress–strain relationship for an orthotropic material can be expressed as follows.

$$\left(\begin{array}{c}{\sigma }_{11}\\ {\sigma }_{22}\\ {\sigma }_{33}\\ {\sigma }_{23}\\ {\sigma }_{31}\\ {\sigma }_{12}\end{array}\right)=\left(\begin{array}{c}{c}_{11}\\ c_{12}\\ c_{13}\\ 0\\ 0\\ 0\end{array}\begin{array}{c}{c}_{12}\\ c_{22}\\ c_{23}\\ 0\\ 0\\ 0\end{array}\begin{array}{c}{c}_{13}\\ c_{23}\\ c_{33}\\ 0\\ 0\\ 0\end{array}\begin{array}{c}0\\ 0\\ 0\\ c_{44}\\ 0\\ 0\end{array}\begin{array}{c}0\\ 0\\ 0\\ 0\\ c_{55}\\ 0\end{array}\begin{array}{c}0\\ 0\\ 0\\ 0\\ 0\\ c_{66}\end{array}\right)\left(\begin{array}{c}{\epsilon }_{11}\\ {\epsilon }_{22}\\ {\epsilon }_{33}\\ {\epsilon }_{23}\\ {\epsilon }_{31}\\ {\epsilon }_{12}\end{array}\right)$$

(4)

The mechanical properties can be represented by C_ij, and in finite element analysis, if the values of E₁, E₂, E₃, G₁₂, G₂₃, G₃₁, and ν_ij (i, j = 1, 2, 3) are known for each element, the relationship between the components of the general anisotropic elastic tensor and the anisotropic engineering constant is as follows:

$$C_{11}={\displaystyle \frac{1-{\nu }_{23}{\nu }_{32}}{E_2{E}_3\mathsf{\Delta }}},C_{22}={\displaystyle \frac{1-{\nu }_{13}{\nu }_{31}}{E_1{E}_3\mathsf{\Delta }}},C_{33}={\displaystyle \frac{1-{\nu }_{12}{\nu }_{21}}{E_1{E}_2\mathsf{\Delta }}},$$

$$C_{12}={\displaystyle \frac{{\nu }_{12}+{\nu }_{31}{\nu }_{23}}{E_2{E}_3\mathsf{\Delta }}}={\displaystyle \frac{{\nu }_{12}+{\nu }_{32}{\nu }_{13}}{E_1{E}_3\mathsf{\Delta }}}$$

$$C_{23}={\displaystyle \frac{{\nu }_{12}+{\nu }_{31}{\nu }_{23}}{E_2{E}_3\mathsf{\Delta }}}={\displaystyle \frac{{\nu }_{12}+{\nu }_{32}{\nu }_{13}}{E_1{E}_3\mathsf{\Delta }}}$$

$$C_{13}={\displaystyle \frac{{\nu }_{12}+{\nu }_{31}{\nu }_{23}}{E_2{E}_3\mathsf{\Delta }}}={\displaystyle \frac{{\nu }_{12}+{\nu }_{32}{\nu }_{13}}{E_1{E}_3\mathsf{\Delta }}}$$

$$C_{44}=G_{23},C_{55}=G_{31},C_{66}=G_{12}$$

where Δ $={\displaystyle \frac{1-{\nu }_{12}{\nu }_{21}-{\nu }_{23}{\nu }_{32}-{\nu }_{31}{\nu }_{13}-{{2\nu }_{21}\nu }_{32}{\nu }_{13}}{E_1{E}_2{E}_3}}$.

To define the properties of an orthotropic material, nine elasticity tensors are required, namely C₁₁, C₂₂, C₃₃, C₄₄, C₅₅, C₆₆, C₁₂, C₁₃, C₂₃ [19,20]. In finite element analysis, mechanical property characteristic values (E₁, E₂, E₃, G₁₂, G₂₃, G₃₁, ν_ij (i, j = 1, 2, 3)) were predicted using the orientation distribution of glass fibers obtained from injection molding process simulation results at positions corresponding to each element, utilizing GEODICT. These predicted mechanical property values were then used in structural analysis.

RVE modeling was conducted using the FiberGeo module of the GeoDict software. The key parameters include fiber diameter, fiber length, fiber volume fraction, and the fiber orientation tensor values.

In the injection molding simulation of the motor mount, fiber orientation tensor results were obtained for each mesh element using SIGMAsoft software. The orientation ratio in the primary flow direction varied across the model, ranging from approximately 35% to 90%. However, due to the computational limitations of generating a unique RVE model for each element, a representative approach was adopted.

Elements with fiber orientation ratios between 35% and 40% were grouped and modeled using an RVE corresponding to 40% orientation. Similarly, elements with orientation ratios of 81% or higher were modeled using the 90% orientation RVE. Intermediate ranges were assigned to the nearest 10% increment (e.g., 50%, 60%, 70%, etc.).

In the RVE modeling, the X-axis value of the fiber orientation tensor was used as the primary reference for flow direction alignment. The Y-axis and Z-axis components were held constant across all RVE models to maintain consistency in transverse dispersion. This approach allowed for a practical yet representative mapping of fiber orientation effects into the multi-scale simulation framework.

Table 7. Fiber orientation tensor values for RVE modeling.

Fiber Orientation Ratio (Based on the X-Axis)	Fiber Orientation Tensor Value
	X-Axis	Y-Axis	Z-Axis
90%	0.9	0.05	0.05
80%	0.8	0.1	0.1
70%	0.7	0.15	0.15
60%	0.6	0.2	0.2
50%	0.5	0.25	0.25
40%	0.4	0.3	0.3

summarizes the fiber orientation tensor values used for each RVE model. The table presents the representative orientation ratio ranges, the corresponding X-axis tensor values applied in the RVE generation, and the fixed Y and Z components. This classification enabled efficient yet accurate integration of orientation-dependent mechanical behavior into the multi-scale analysis.

2.4.3. Simulation Process

Figure 9 illustrates the simulation workflow, spanning from injection molding process simulation to structural simulation. The injection molding simulation was conducted using SIGMASoft, employing a material card for PA66/GF50 (wt%) provided by DatapointLabs (Ithaca, NY, USA).

The mesh model generated for injection molding analysis cannot typically be directly used for structural simulation due to differences in modeling requirements. Therefore, residual stress results were generated for each element of the mesh model during the injection molding simulation. These results were then mapped onto the corresponding elements of the structural analysis mesh model, which was created using Abaqus. The mapping process was performed using the mapping module provided by SIGMASoft.

The fiber orientation tensor results were further utilized in the structural simulation to define orthotropic material properties. Specifically, the orientation tensor values were used to assign directional elastic moduli (E₁, E₂, E₃) for each element in the structural mesh model.

The injection molding analysis results, along with information such as fiber orientation and residual stress, were utilized in structural analysis. In structural analysis, interpretations were conducted for tension specimens at 0 degrees, 45 degrees and 90 degrees with respect to the flow direction, based on flat specimens. Additionally, analyses were performed for the hammering test on the motor mount bracket product.

3. Results and Discussion

3.1. RVE-Based Prediction of Orthotropic Material Properties for PA66/GF50 (wt%)

The fiber volume fraction was set to 32%, and periodic boundary conditions were applied to ensure accurate homogenization. FEA was performed to extract the orthotropic stiffness matrix, from which the elastic moduli, Poisson’s ratios, and shear moduli were calculated.

Figure 10 illustrates the RVE model generation results for different fiber orientation ratios, visually representing the microstructural variations.

Table 8. Orthotropic material properties for PA66/GF50 (wt%).

X-Axis (Ratio)	${\mathit{E}}_1$ (GPa)	${\mathit{E}}_2$ (GPa)	${\mathit{E}}_3$ (GPa)	${\mathit{\nu }}_{12}$	${\mathit{\nu }}_{13}$	${\mathit{\nu }}_{23}$	${\mathit{\nu }}_{21}$	${\mathit{\nu }}_{31}$	${\mathit{\nu }}_{23}$	${\mathit{G}}_{12}$ (GPa)	${\mathit{G}}_{13}$ (GPa)	${\mathit{G}}_{23}$ (GPa)
90%	9.881	3.497	3.507	0.387	0.386	0.499	0.137	0.137	0.499	1.358	1.371	1.132
80%	8.564	3.736	3.677	0.384	0.398	0.499	0.167	0.171	0.499	1.526	1.537	1.229
70%	7.461	3.929	3.982	0.391	0.384	0.469	0.206	0.205	0.476	1.615	1.629	1.327
60%	6.424	4.053	4.113	0.388	0.384	0.437	0.245	0.246	0.443	1.676	1.719	1.427
50%	5.632	4.290	4.225	0.373	0.383	0.412	0.284	0.287	0.406	1.722	1.727	1.535
40%	4.967	4.462	4.484	0.366	0.368	0.375	0.329	0.332	0.379	1.699	1.719	1.620

presents the corresponding orthotropic material properties derived from each RVE model, which are used to assign accurate anisotropic behavior in the FEM analysis. The RVE cubes are therefore not arbitrary but are directly linked to the fiber orientation tensor values obtained from injection molding simulation. Each RVE cube corresponds to a specific fiber orientation ratio in the primary flow direction (X-axis), and the table provides the resulting orthotropic elastic constants (E₁, E₂, E₃), Poisson’s ratios (ν₁₂, ν₁₃, ν₂₃, etc.), and shear moduli (G₁₂, G₁₃, G₂₃). As the fiber orientation ratio increases from 40% to 90%, a clear trend is observed: the stiffness in the flow direction (E₁) increases significantly, from 4.97 GPa at 40% to 9.88 GPa at 90%. This demonstrates the strong anisotropic behavior of the composite and highlights the importance of accurately capturing fiber orientation in multi-scale modeling.

3.2. Experimental Test Results and Simulation Results

As shown in Figure 11, the tensile test results of flat-molded specimens in different flow directions reveal distinct stress–strain responses. These differences clearly demonstrate the anisotropic mechanical behavior of the material, which is strongly influenced by the fiber orientation resulting from the injection molding process.

Figure 12 presents the comparison between experimental tensile test results and simulation predictions for specimens oriented at 0°, 45°, and 90° relative to the injection flow direction. The simulation demonstrates high reliability in capturing the anisotropic mechanical behavior of short fiber-reinforced polymer (SFRP) composites. The flat specimen geometry used in the simulation matches that of the actual test specimens, allowing for direct validation of the fiber direction-dependent mechanical response.

Figure 13 illustrates the injection molding simulation results, highlighting the influence of flow patterns on fiber orientation distribution. The simulation provides detailed outputs including fiber orientation tensors, shrinkage, warpage, residual stresses, and the principal direction ratio (SIGMAsoft Max. Eigenvalue). These parameters are visualized across the molded part and are critical for understanding the internal structure and anisotropic behavior of the composite.

The fiber orientation is shown to align strongly with the injection flow, particularly in regions of high shear near the gate. This directional alignment significantly affects local mechanical properties. The integration of these simulation results into the finite element method (FEM) framework enables accurate mapping of material properties, improving the predictive capability for structural performance under real-world loading conditions.

The simulation results for the product, as shown in Figure 14, can be observed to closely match the test results in terms of fracture location. The strength analysis results show tensile strength of 23.8 kN, and compressive strength of 26.5 kN, with a reliability level of approximately 93%.

To further validate the dynamic stiffness characteristics, hammering tests and FRF (frequency response function) analysis were conducted, as illustrated in Figure 15.

In mode analysis, accurate representation of anisotropic stiffness can enhance the reliability of predicting dynamic stiffness since it is predominantly influenced by the M (mass) and K (structure stiffness) characteristics.

3.3. Discussion

This study addresses several key technical challenges in accurately predicting the anisotropic mechanical behavior of SFRP composites. One of the primary challenges lies in capturing the complex relationship between fiber orientation strongly influenced by the injection molding process and the resulting mechanical properties. To overcome this, we employed a multi-scale modeling approach that integrates fiber orientation tensor data from injection molding simulations into representative volume element RVE-based FEA analysis. This integration allows for the derivation of orthotropic material properties that reflect the actual microstructural characteristics of the molded part.

A notable innovation in this study is the direct mapping of fiber orientation data to RVE models, enabling the prediction of direction-dependent stiffness values. As demonstrated in Table 8, the elastic modulus in the primary flow direction (E₁) increases significantly with higher fiber alignment, confirming the strong anisotropic behavior of the composite. This highlights the importance of incorporating process-informed microstructural data into structural simulations.

Another technical advancement is the validation of simulation results through both static and dynamic experimental tests. The tensile and compressive test results show strong agreement with simulation predictions, particularly in terms of fracture location and strength values. To quantitatively assess this agreement, we compared the maximum tensile stress values from both experimental and simulation data across three fiber orientations (0°, 45°, and 90°). The calculated mean absolute error (MAE) was approximately 6.67 MPa, and the root mean square error (RMSE) was approximately 7.07 MPa, indicating a high level of accuracy in the static mechanical predictions.

Furthermore, the use of frequency response function (FRF) analysis and hammering tests provides additional confirmation of the model’s ability to capture dynamic stiffness characteristics, which are highly sensitive to anisotropic stiffness distributions. The estimated MAE and RMSE for the frequency response in the X, Y, and Z directions were approximately 1.0 dB/g, further validating the model’s predictive capability in dynamic conditions.

Compared to conventional modeling approaches that assume isotropic or simplified anisotropic behavior, our method offers a more accurate and scalable framework for predicting the performance of SFRP components under real-world loading conditions. This is particularly valuable in automotive applications, where material behavior must be precisely understood to ensure safety and performance.

4. Conclusions

The findings of this study collectively confirm that the integration of process-informed fiber orientation data into a multi-scale modeling framework enables a highly accurate prediction of both static and dynamic mechanical behavior in SFRP components. The simulation results, validated through tensile and compressive testing as well as dynamic modal analysis, demonstrate strong agreement with experimental observations, particularly in terms of fracture location, strength values, and vibrational response.

To quantitatively evaluate the accuracy of the simulations, error metrics were calculated for both static and dynamic tests. For tensile strength predictions across three fiber orientations (0°, 45°, and 90°), the mean absolute error (MAE) and root mean square error (RMSE) were approximately 6.67 MPa and 7.07 MPa, respectively. In dynamic hammering tests, the estimated MAE and RMSE for frequency response in the X, Y, and Z directions were approximately 1.0 dB/g, further validating the model’s predictive capability.

The ability to reflect anisotropic stiffness characteristics, influenced by fiber orientation and molding conditions, significantly enhances the reliability of structural simulations. This approach not only supports the prediction of performance variations due to changes in fiber content, gate position, and part geometry, but also facilitates the design and optimization of composite materials tailored to specific functional requirements. Therefore, the proposed methodology provides a robust and scalable foundation for advancing the predictive engineering of fiber-reinforced polymer components in automotive and other high-performance applications.