Enhancing Finite Element Simulations of 3D-Printed PLA Using PINN: Validated Through Experimental Testing

Enhancing Finite Element Simulations of 3D-Printed PLA Using PINN: Validated Through Experimental Testing | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Enhancing Finite Element Simulations of 3D-Printed PLA Using PINN: Validated Through Experimental Testing Mohammad Hadi Zahmatkeshan, Farid Reza Biglari, Bijan Mollaei Dariani This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6474572/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The accuracy of finite element analysis (FEA) simulations for 3D-printed parts is often limited by assumptions regarding the material's mechanical properties, particularly when these properties are derived from conventional injection-molded specimens rather than directly measured from 3D-printed components. The acquisition of precise mechanical properties for FEA requires testing 3D-printed samples that exactly replicate printing parameters such as raster angle and infill density and layer thickness, which is a time-consuming and expensive procedure. The research presents an advanced technique that improves FEA simulation precision for PLA 3D-printed part tensile strength through Advanced Physics-Informed Neural Networks (PINN). Experimental tensile test data from various raster angles, infill densities, and layer thicknesses enable us to train a PINN for material property prediction which could differ substantially from traditional injection-molded PLA properties. The approach enables the prediction of tensile strength across various printing options while eliminating the requirement for additional physical tests. The research demonstrates that combining PINNs with standard FEA techniques leads to better simulation accuracy and represents a budget-friendly alternative to direct testing. The proposed method demonstrates how machine learning technology speeds up computational methods while addressing the precise modeling challenges of 3D-printed materials. Physics Informed Neural Networks Finite Element Analysis Additive manufacturing Machine learning Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction The mechanical properties of 3D-printed components is highly dependent on process parameters such as raster angle, infill density, and layer thickness. Because of the layer-by-layer deposition process, fused deposition modeling (FDM) introduces anisotropy, in contrast to classical injection molding, where material characteristics are rather homogeneous [ 1 , 2 , 3 ]. Therefore, it's still difficult to forecast the mechanical behavior of FDM-printed components with accuracy, especially when utilizing numerical simulations such as the Finite Element Method (FEM) in Abaqus [4]. The mechanical characteristics of injection-molded specimens are frequently used as input material data in simulation studies, supposing uniformity across all printing conditions. However, because it ignores the complex microstructural effects brought about by various printing conditions, this simplification frequently results in differences between simulation and actual findings [4,5]. The mechanical characteristics of each unique combination of raster angle, infill, and layer thickness would need to be empirically determined in order to get appropriate simulation results; this is a method that is not cost-effective or scalable[6]. This study provide a Physics-Informed Neural Network (PINN) architecture that combines experimental and numerical data to improve the prediction accuracy of Abaqus simulations, therefore overcoming these constraints and speeding up process. By fusing physical governing equations with machine learning methods, PINNs enable the model to understand the connection between mechanical properties observed experimentally and those anticipated by simulation [7,8]. The model can adjust Abaqus-simulated values for new printing configurations without the need for extra experimental testing by training the PINN using a collection of experimental stress-strain curves and related finite element (FE) simulations [9,10]. Physics-Informed Neural Networks (PINNs) have been used in recent studies to model anisotropic materials and laminated composites by directly integrating the physical principles controlling them into the neural networks. This method enables effective simulations in stress-strain analysis and structural health monitoring [11]. In additive manufacturing processes, PINNs have also been successfully used to represent time-dependent material characteristics, providing quicker computation and flexibility in response to shifting process factors [12,13]. Recent studies have increased the number of engineering domains in which PINNs may be used. For instance, compared to conventional techniques, Std-PINNs for plasma simulations have shown improved accuracy [14]. It has been suggested that integrating finite difference techniques with PINNs can provide competitive accuracy at a lower cost than more conventional methods [15]. Inverse issues like determining damping and elastic modulus in beam constructions have been solved using PINNs in structural dynamics [16]. For material model calibration, PINNs have also been used to calibrate linear-elastic models from displacement data in almost real-time [17]. Similarly, in computational elastodynamics, PINNs are solving elastodynamic problems without labeled data, addressing complex boundary conditions [18]. An important development in computational mechanics is the combination of PINNs and Finite Element Analysis (FEA). PINNs directly integrate physical principles into the neural network's loss function, in contrast to conventional machine learning techniques that depend on data-driven models [19]. In contrast to other machine learning methods that might not generalize to novel or unknown contexts, this guarantees that solutions are compatible with governing equations, such as partial differential equations (PDEs) [20]. Because PINNs employ well-established physics, they also require a lot less training data than traditional machine learning techniques, which makes them especially helpful in fields with a lack of experimental data [22,21]. In addition, PINNs can tackle inverse problems, like parameter estimation, without a need for iterative forward simulations which is a limitation of the majority of machine learning models [23]. Although PINNs are computationally expensive, recent improvements, like domain decomposition and adaptive training algorithms, have made them considerably more efficient, putting them at a level with other machine learning methods for solving challenging partial differential equations (PDEs) [24]. This work presents a hybrid numerical approach that uses scientific machine learning to improve FEA predictions while lowering processing costs and increasing accuracy. While preserving high-fidelity predictions of the mechanical response of 3D-printed PLA, the suggested technique may greatly reduce the requirement for intensive experimental testing. Our approach is in line with the increasing need for numerical solvers enhanced by machine learning and the application of data-driven models to speed up computational methods in scientific computing. Methodology 3.1 Experimental Data Collection In accordance with ISO527, the experimental protocol was created to obtain stress-strain data for several 3D-printed PLA specimens under tensile loading [25]. A FDM 3D printer “Promex50” was used to create the specimens, and PLA filament Creality Hyper Speed was chosen since it is often used in FDM 3D printing. The Young’s modulus, yield stress, and strain values were predicted using a Physics-Informed Neural Network (PINN) model trained on experimental data. These predicted properties were then used as input for finite element analysis (FEA). Various infill percentages such as (60%,70%,80%,90%,100%) were used to study their effects on mechanical properties. Layer thicknesses varied across specimens, which were printed at various raster angles, such as 0°, 45°, ± 45°, 60°, 75°, and 90° (0.25 mm, 0.3 mm, 0.35 mm, and 0.4 mm). Tensile tests were performed in accordance with ISO527 requirements using a Universal Testing Machine “Santam20”. The specimens were subjected to uniaxial tensile loading, and stress-strain data were collected. The results from the first set of tests (51 specimens) were used to train the model, while the second series of tests (8 specimens) was used to validate the predicted stress-strain behavior by finite element analysis assisted by the PINN model. 3.2 PINN-Based Mechanical Property Prediction A Physics-Informed Neural Network (PINN) was developed to predict the mechanical properties of 3dprinted specimens under universal tensile testing in order to improve the precision of finite element analysis (FEA) simulations. The PINN framework integrates both data-driven learning and physics-based constraints to ensure physically consistent predictions of stress-strain behavior. Three important printing parameters including raster angle, infill percentage, and layer thickness, were used to train the model. These process parameters were chosen to represent the anisotropic behavior of FDM 3dprinted structures and have a major impact on the mechanical properties of 3D-printed objects. The model outputs are: Yield stress, plastic strain, and Young's modulus. Network Architecture and Training Strategy : To provide nonlinearity and improve learning, the neural network design included ReLU activation functions in several fully connected layers. In order to uncover intricate correlations between input properties and mechanical reactions, the hidden layers were created with an increasing number of neurons. To prevent issues related to vanishing gradients, the network weights were initialized using Xavier initialization. The training process used an adaptive optimization strategy, employing the Adam optimizer with an initial learning rate of 0.01. To provide smoother convergence and avoid overfitting, a step learning rate scheduler was used to progressively reduce the learning rate. The primary loss function for minimizing differences between expected stress-strain values and actual data was the Mean Squared Error (MSE). Physics-Informed Constraints : The PINN integrated physics-informed loss terms to match known material behavior unlike traditional neural networks. The physics-based loss function was based on Hooke's Law according to reference [26]. The model imposed penalties on deviations from fundamental material laws to guarantee realistic predictions of stress-strain behavior. A decay function was used to adaptively weight the physics loss term so its impact diminished over time as the model absorbed experimental data. Evaluation Metrics and Validation : To ensure an objective evaluation of the model's generalizability, this validation dataset contained four tensile test results from specimens that were excluded from the training phase. The coefficient of determination (R2), which measures the percentage of variance explained by the model; the root mean squared error (RMSE), which rates the average magnitude of prediction errors; and the mean absolute error (MAE), which rates the average absolute deviation from the true values, were the three main evaluation metrics taken into consideration in order to gauge its performance. By fusing data-driven learning with physics-based constraints, the physics-informed neural network (PINN) achieved better generalization than empirical models alone. The resulting trained model was an effective predictive means for mechanical property prediction from print parameters, enabling more precise finite element analysis (FEA) simulations without the requirement of extensive experimental datasets. 3.3 FEA Simulation in Abaqus The obtained mechanical properties from the PINN model were subsequently employed as input parameters for the FEA simulations in Abaqus. The (C3D8R) Elements were defined for the PLA samples to clearly demonstrate the stress and deformation distribution. the features predicted by the PINN are applied into the mechanical properties module and a fine mesh has been imposed in order to obtain precise stress-strain predictions, whilst the mesh is being refined for reasonable computational efficiency. In the tensile test, one side of the specimen was fixed by clamping, while the other side was pulled in a displacement-controlled manner. A displacement was then applied to match experimental conditions for direct comparison. In addition, to further improve the simulation of thermal and mechanical response, enabling more realistic simulation of heat conduction and material response to mechanical loading, the UMATH, DFLUX and UMAT subroutines were also invoked (Holmes et al., 2022). 3.4 Validation Using Experimental Testing In order to validate the proposed methodology, tensile tests were conducted on eight printed specimens (Fig. 2 ) with different printing parameters. The results from these tests were compared to both the PINN-predicted mechanical properties (Table.1) and the FEA simulations (Fig. 4 ) to determine accuracy. The experimental stress-strain curves were compared to the FEA results, and differences were analyzed to evaluate the effectiveness of using PINN-predicted properties in FEA. The main goal was to determine whether the PINN-enhanced FEA approach improves accuracy in comparison to using uniform material properties. A digital twin was established to enhance the simulation accuracy of 3D-printed PLA parts by integrating PINN-predicted material properties into the FEA model. The model could predict mechanical properties for any raster angle, layer thickness, and infill density without any additional testing after training. The digital twin saves time-consuming trial testing by allowing the optimization of print parameters for desired mechanical properties. The technology provides an alternative to conventional trial-and-error procedures to predict the performance of 3D-printed parts earlier and more accurately. Results and Discussion The training of the APINN model successfully minimized the combined loss function over the course of 5000 epochs, thereby showing the regular successfulness of the model in learning both data and physical laws in a gradual manner. At first, the mean squared error (MSE) loss was high at 0.18046, indicating that the predicted values and the experimental data are not equated. However, as training progressed, the MSE loss decreased to 0.03664 by the final epoch which is much less than the initial value. The decrease of MSE loss could be seen as a consequence of the model's adaptation which came as a result of increased data, which permitted the model to better approximate the mechanical properties of the material. Meanwhile, the physics-informed loss showed a steady decrease from 0.00723 at epoch 0 to 0.00214 by epoch 4500. This is a sign that the addition of physical constraints, i.e., the stress-strain response of the material, was instrumental in guiding the model towards better predictive capability. The physics loss acts as a regularizer, stopping overfitting and making sure the prediction made by the model is not solely data-dependent but also physically realizable. The reduction of the total loss from 0.18769 at epoch 0 to 0.03751 at epoch 4500 also indicated that the model was converging to an optimal solution. The coupled loss function, made up of experimental data along with physics-informed terms, managed to combine data-driven model training with physical law preservation. These results demonstrate the capacity of the Advanced PINN model for bridging experimental data with physical laws, augmenting predictive precision with physical consistency in the output. 4.1 Evaluation of the PINN-Powered FEA Approach This study's main goal was to improve finite element analysis (FEA) accuracy by including mechanical characteristics that an Advanced Physics-Informed Neural Network (APINN) predicted. Initially, a wide range of experimentally acquired stress-strain responses from 3D-printed PLA specimens with varying raster angles, infill densities, and layer thicknesses were used to train the PINN model. After training, the mechanical characteristics for particular print configurations were predicted by the PINN and utilized as input parameters for the Abaqus FEA simulations. To validate the effectiveness of this approach, we tested eight distinct specimens with varying raster angles, layer thicknesses, and infill densities. The mechanical properties predicted by the PINN were utilized in the FEA model, and the simulation results were compared against experimental tensile test data. as shown in Figure.4 The comparison aimed to determine using PINN-enhanced material properties in FEA could yield more accurate predictions aligned with experimental observations. 4.2 Comparison of FEA Predictions with Experimental Data The stress-strain behavior obtained from the FEA simulations showed a significant improvement in accuracy compared to traditional FEA methods that assume uniform material properties. The incorporation of PINN-predicted mechanical properties enabled the FEA model to capture the anisotropic behavior of 3D-printed PLA specimens more effectively. Table.1 below summarizes the predicted strain and stress values from FEA compared to the experimentally measured values: Table 1 comparison table along with error calculations (Absolute Error for Strain and Stress) Raster Angle (°) Layer Thickness (mm) Infill (%) FEA Predicted Strain Experimental Strain Absolute Error (Strain) FEA Predicted Stress (MPa) Experimental Stress (MPa) Absolute Error (Stress) 50 0.3 75 1.8192 1.8691 0.0499 34.52 34.15 0.37 45 0.4 70 1.7929 1.8349 0.0420 34.73 34.42 0.31 30 0.35 80 1.8320 1.8565 0.0245 36.18 35.84 0.34 ± 45 0.25 60 1.5610 1.5236 0.0374 36.05 36.87 0.82 60 0.4 70 1.7928 1.7821 0.0107 34.39 34.52 0.13 0 0.4 100 1.6705 1.6321 0.0384 35.69 35.49 0.8 75 0.3 65 1.6634 1.6205 0.0429 35.67 35.38 0.71 90 0.4 80 1.1508 1.1371 0.0137 33.15 33.02 0.13 Key Observations: The absolute errors for strain and stress are relatively small, demonstrating the accuracy of the PINN model. The largest deviation occurs at Raster Angle ± 45° and 0°, which might be due to anisotropic effects in the printed material. 90° raster angle shows the smallest errors, indicating the model's better predictive accuracy for this configuration. Table 2 The error metrics for the strain and stress data Metric Strain Stress MAE 0.0324 0.4963 RMSE 0.0351 0.5965 R² 0.9766 0.7037 The values in Table.2 represents the precision of the PINN-based FEA simulation in determining the mechanical properties of PLA 3dprinted specimens. The small Mean Absolute Error for strain (0.0324) indicates that the predicted value for strain closely coincides with the experimental results with minimal deviation. Likewise, the accuracy of the model is once more demonstrated by the low Root Mean Square Error value for strain (0.0351). Strong agreement between predicted and experimental values is revealed by the high R2 value for strain (0.9766), confirming the model's applicability in simulating strain behavior. Although the R² value for stress (0.7037) is less, indicating some fluctuation in stress predictions, overall agreement remains strong. More importantly, the variation between FEA-predicted and experimental stress values was within an acceptable range, supporting the effectiveness of this approach. These findings highlight the model's capability as well as suggest areas for further improvement, particularly in stress prediction. Conclusion In order to increase the prediction’s precision of the stress-strain behavior for 3dprinted PLA specimens, this study effectively integrated Finite Element Analysis (FEA) with an advanced Physics-Informed Neural Network (PINN). By training the PINN on actual experimental data the model was able to capture how 3D-printed materials exhibit anisotropic behavior across different printing conditions such as raster angles, layer thicknesses and infill densities. The use of PINN to predict strain and stress behavior, based on print configurations (raster angles, layer thicknesses, and infill densities),as abaqus material property input, the predictive capabilities of the FEA simulation is significantly improved .The PINN-predicted properties were incorporated into Abaqus simulations and compared against experimental tensile test data, revealing a high degree of agreement between the two. The key benefits of this approach are: PINN-enhanced FEA simulations showed noticeably better agreement with experimental data when compared to conventional FEA techniques that assume average material characteristics. By training the PINN model on varied datasets that capture the anisotropic nature of 3D-printed PLA, the predicted mechanical properties more accurately reflect the behavior of specimens under tensile loading. This approach allows for the estimation of stress-strain behavior of 3Dprinted objects, across different printing configurations without requiring new experimental testing, which saves both time and resources. The method works across multiple 3D printing parameters which makes it highly adaptable for use in design and production operations. The results state that the integration of FEA with PINN is a solution with a lot of potential and is a good method for doing simulations and predictions of 3D printed parts. This method can be applied to a more detailed, efficient, and reliable simulation in the additive manufacturing. Also, other studies are possible to be conducted that will try this approach on other materials and shapes or to use machine learning in order to refine the material property prediction. Declarations Author Contribution M.H. Zahmatkeshan conducted the research, performed the simulations, analyzed the results, and wrote the main manuscript text. Associate Professor. F.R.Biglari and Professor B. Mollaei Dariani served as the primary and secondary supervisors, respectively, providing guidance and critical revisions throughout the research process. All authors reviewed and approved the final manuscript. Data Availability The data that support the findings of this study, including simulation results and experimental test data, are available from the corresponding author upon reasonable request. References Lokesh, N., Praveena, B. A., Reddy, J. S., Vasu, V. K., & Vijaykumar, S. (2022). Evaluation on effect of printing process parameter through Taguchi approach on mechanical properties of 3D printed PLA specimens using FDM at constant printing temperature. Materials today: proceedings , 52 , 1288-1293. Leite, M., Fernandes, J., Deus, A. M., Reis, L., & Vaz, M. F. (2018). Study of the influence of 3D printing parameters on the mechanical properties of PLA. Rouf, S., Raina, A., Haq, M. I. U., Naveed, N., Jeganmohan, S., & Kichloo, A. F. 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2","display":"","copyAsset":false,"role":"figure","size":85790,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental validation of the proposed approach using eight specimens tested across different printing configuration\u003c/p\u003e\n\u003cp\u003e(from left, rasters: 75°,60°,±45°,45°,90°,30°,50°,0°) \u0026nbsp;.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6474572/v1/a9809384592012b9826b34a1.jpg"},{"id":82005961,"identity":"0389ed83-7170-4b55-b1e7-39d71fa677ed","added_by":"auto","created_at":"2025-05-05 22:27:17","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":84327,"visible":true,"origin":"","legend":"\u003cp\u003eConvergence of Physics-Informed Loss during Training\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6474572/v1/182c4e5c50ee557233bc1744.jpg"},{"id":82005781,"identity":"4acd72bd-c073-4330-a4e7-bafd0b4ad339","added_by":"auto","created_at":"2025-05-05 22:11:17","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":103506,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of stress-strain curves from experimental data and PINN-based FEA simulations.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6474572/v1/67e3e4b08b43bd87a99f71a6.jpg"},{"id":83086217,"identity":"491a99c1-fb9c-4c47-9f09-40ad9fc3bbd8","added_by":"auto","created_at":"2025-05-19 23:31:18","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":960476,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6474572/v1/c6b1eb18-90cf-4527-84a4-6a237b593b13.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Enhancing Finite Element Simulations of 3D-Printed PLA Using PINN: Validated Through Experimental Testing","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe mechanical properties of 3D-printed components is highly dependent on process parameters such as raster angle, infill density, and layer thickness. Because of the layer-by-layer deposition process, fused deposition modeling (FDM) introduces anisotropy, in contrast to classical injection molding, where material characteristics are rather homogeneous [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Therefore, it's still difficult to forecast the mechanical behavior of FDM-printed components with accuracy, especially when utilizing numerical simulations such as the Finite Element Method (FEM) in Abaqus [4].\u003c/p\u003e \u003cp\u003eThe mechanical characteristics of injection-molded specimens are frequently used as input material data in simulation studies, supposing uniformity across all printing conditions. However, because it ignores the complex microstructural effects brought about by various printing conditions, this simplification frequently results in differences between simulation and actual findings [4,5]. The mechanical characteristics of each unique combination of raster angle, infill, and layer thickness would need to be empirically determined in order to get appropriate simulation results; this is a method that is not cost-effective or scalable[6].\u003c/p\u003e \u003cp\u003eThis study provide a Physics-Informed Neural Network (PINN) architecture that combines experimental and numerical data to improve the prediction accuracy of Abaqus simulations, therefore overcoming these constraints and speeding up process. By fusing physical governing equations with machine learning methods, PINNs enable the model to understand the connection between mechanical properties observed experimentally and those anticipated by simulation [7,8]. The model can adjust Abaqus-simulated values for new printing configurations without the need for extra experimental testing by training the PINN using a collection of experimental stress-strain curves and related finite element (FE) simulations [9,10].\u003c/p\u003e \u003cp\u003ePhysics-Informed Neural Networks (PINNs) have been used in recent studies to model anisotropic materials and laminated composites by directly integrating the physical principles controlling them into the neural networks. This method enables effective simulations in stress-strain analysis and structural health monitoring [11].\u003c/p\u003e \u003cp\u003eIn additive manufacturing processes, PINNs have also been successfully used to represent time-dependent material characteristics, providing quicker computation and flexibility in response to shifting process factors [12,13]. Recent studies have increased the number of engineering domains in which PINNs may be used. For instance, compared to conventional techniques, Std-PINNs for plasma simulations have shown improved accuracy [14]. It has been suggested that integrating finite difference techniques with PINNs can provide competitive accuracy at a lower cost than more conventional methods [15]. Inverse issues like determining damping and elastic modulus in beam constructions have been solved using PINNs in structural dynamics [16]. For material model calibration, PINNs have also been used to calibrate linear-elastic models from displacement data in almost real-time [17]. Similarly, in computational elastodynamics, PINNs are solving elastodynamic problems without labeled data, addressing complex boundary conditions [18].\u003c/p\u003e \u003cp\u003eAn important development in computational mechanics is the combination of PINNs and Finite Element Analysis (FEA). PINNs directly integrate physical principles into the neural network's loss function, in contrast to conventional machine learning techniques that depend on data-driven models [19]. In contrast to other machine learning methods that might not generalize to novel or unknown contexts, this guarantees that solutions are compatible with governing equations, such as partial differential equations (PDEs) [20]. Because PINNs employ well-established physics, they also require a lot less training data than traditional machine learning techniques, which makes them especially helpful in fields with a lack of experimental data [22,21]. In addition, PINNs can tackle inverse problems, like parameter estimation, without a need for iterative forward simulations which is a limitation of the majority of machine learning models [23]. Although PINNs are computationally expensive, recent improvements, like domain decomposition and adaptive training algorithms, have made them considerably more efficient, putting them at a level with other machine learning methods for solving challenging partial differential equations (PDEs) [24].\u003c/p\u003e \u003cp\u003eThis work presents a hybrid numerical approach that uses scientific machine learning to improve FEA predictions while lowering processing costs and increasing accuracy. While preserving high-fidelity predictions of the mechanical response of 3D-printed PLA, the suggested technique may greatly reduce the requirement for intensive experimental testing. Our approach is in line with the increasing need for numerical solvers enhanced by machine learning and the application of data-driven models to speed up computational methods in scientific computing.\u003c/p\u003e"},{"header":"Methodology","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1 Experimental Data Collection\u003c/h2\u003e\n \u003cp\u003eIn accordance with ISO527, the experimental protocol was created to obtain stress-strain data for several 3D-printed PLA specimens under tensile loading [25]. A FDM 3D printer \u0026ldquo;Promex50\u0026rdquo; was used to create the specimens, and PLA filament Creality Hyper Speed was chosen since it is often used in FDM 3D printing. The Young\u0026rsquo;s modulus, yield stress, and strain values were predicted using a Physics-Informed Neural Network (PINN) model trained on experimental data. These predicted properties were then used as input for finite element analysis (FEA). Various infill percentages such as (60%,70%,80%,90%,100%) were used to study their effects on mechanical properties. Layer thicknesses varied across specimens, which were printed at various raster angles, such as 0\u0026deg;, 45\u0026deg;, \u0026plusmn;\u0026thinsp;45\u0026deg;, 60\u0026deg;, 75\u0026deg;, and 90\u0026deg; (0.25 mm, 0.3 mm, 0.35 mm, and 0.4 mm). Tensile tests were performed in accordance with ISO527 requirements using a Universal Testing Machine \u0026ldquo;Santam20\u0026rdquo;. The specimens were subjected to uniaxial tensile loading, and stress-strain data were collected. The results from the first set of tests (51 specimens) were used to train the model, while the second series of tests (8 specimens) was used to validate the predicted stress-strain behavior by finite element analysis assisted by the PINN model.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2 PINN-Based Mechanical Property Prediction\u003c/h2\u003e\n \u003cp\u003eA Physics-Informed Neural Network (PINN) was developed to predict the mechanical properties of 3dprinted specimens under universal tensile testing in order to improve the precision of finite element analysis (FEA) simulations. The PINN framework integrates both data-driven learning and physics-based constraints to ensure physically consistent predictions of stress-strain behavior. Three important printing parameters including raster angle, infill percentage, and layer thickness, were used to train the model. These process parameters were chosen to represent the anisotropic behavior of FDM 3dprinted structures and have a major impact on the mechanical properties of 3D-printed objects. The model outputs are: Yield stress, plastic strain, and Young\u0026apos;s modulus.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eNetwork Architecture and Training Strategy\u003c/strong\u003e:\u003c/p\u003e\n \u003cp\u003eTo provide nonlinearity and improve learning, the neural network design included ReLU activation functions in several fully connected layers. In order to uncover intricate correlations between input properties and mechanical reactions, the hidden layers were created with an increasing number of neurons. To prevent issues related to vanishing gradients, the network weights were initialized using Xavier initialization.\u003c/p\u003e\n \u003cp\u003eThe training process used an adaptive optimization strategy, employing the Adam optimizer with an initial learning rate of 0.01.\u003c/p\u003e\n \u003cp\u003eTo provide smoother convergence and avoid overfitting, a step learning rate scheduler was used to progressively reduce the learning rate. The primary loss function for minimizing differences between expected stress-strain values and actual data was the Mean Squared Error (MSE).\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003ePhysics-Informed Constraints\u003c/strong\u003e:\u003c/p\u003e\n \u003cp\u003eThe PINN integrated physics-informed loss terms to match known material behavior unlike traditional neural networks. The physics-based loss function was based on Hooke\u0026apos;s Law according to reference [26]. The model imposed penalties on deviations from fundamental material laws to guarantee realistic predictions of stress-strain behavior. A decay function was used to adaptively weight the physics loss term so its impact diminished over time as the model absorbed experimental data.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eEvaluation Metrics and Validation\u003c/strong\u003e:\u003c/p\u003e\n \u003cp\u003eTo ensure an objective evaluation of the model\u0026apos;s generalizability, this validation dataset contained four tensile test results from specimens that were excluded from the training phase. The coefficient of determination (R2), which measures the percentage of variance explained by the model; the root mean squared error (RMSE), which rates the average magnitude of prediction errors; and the mean absolute error (MAE), which rates the average absolute deviation from the true values, were the three main evaluation metrics taken into consideration in order to gauge its performance.\u003c/p\u003e\n \u003cp\u003eBy fusing data-driven learning with physics-based constraints, the physics-informed neural network (PINN) achieved better generalization than empirical models alone. The resulting trained model was an effective predictive means for mechanical property prediction from print parameters, enabling more precise finite element analysis (FEA) simulations without the requirement of extensive experimental datasets.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e3.3 FEA Simulation in Abaqus\u003c/h2\u003e\n \u003cp\u003eThe obtained mechanical properties from the PINN model were subsequently employed as input parameters for the FEA simulations in Abaqus. The (C3D8R) Elements were defined for the PLA samples to clearly demonstrate the stress and deformation distribution. the features predicted by the PINN are applied into the mechanical properties module and a fine mesh has been imposed in order to obtain precise stress-strain predictions, whilst the mesh is being refined for reasonable computational efficiency. In the tensile test, one side of the specimen was fixed by clamping, while the other side was pulled in a displacement-controlled manner. A displacement was then applied to match experimental conditions for direct comparison. In addition, to further improve the simulation of thermal and mechanical response, enabling more realistic simulation of heat conduction and material response to mechanical loading, the UMATH, DFLUX and UMAT subroutines were also invoked (Holmes et al., 2022).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e3.4 Validation Using Experimental Testing\u003c/h2\u003e\n \u003cp\u003eIn order to validate the proposed methodology, tensile tests were conducted on eight printed specimens (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e) with different printing parameters. The results from these tests were compared to both the PINN-predicted mechanical properties (Table.1) and the FEA simulations (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e) to determine accuracy. The experimental stress-strain curves were compared to the FEA results, and differences were analyzed to evaluate the effectiveness of using PINN-predicted properties in FEA. The main goal was to determine whether the PINN-enhanced FEA approach improves accuracy in comparison to using uniform material properties.\u003c/p\u003e\n \u003cp\u003eA digital twin was established to enhance the simulation accuracy of 3D-printed PLA parts by integrating PINN-predicted material properties into the FEA model. The model could predict mechanical properties for any raster angle, layer thickness, and infill density without any additional testing after training. The digital twin saves time-consuming trial testing by allowing the optimization of print parameters for desired mechanical properties. The technology provides an alternative to conventional trial-and-error procedures to predict the performance of 3D-printed parts earlier and more accurately.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Results and Discussion","content":"\u003cp\u003eThe training of the APINN model successfully minimized the combined loss function over the course of 5000 epochs, thereby showing the regular successfulness of the model in learning both data and physical laws in a gradual manner. At first, the mean squared error (MSE) loss was high at 0.18046, indicating that the predicted values and the experimental data are not equated. However, as training progressed, the MSE loss decreased to 0.03664 by the final epoch which is much less than the initial value. The decrease of MSE loss could be seen as a consequence of the model's adaptation which came as a result of increased data, which permitted the model to better approximate the mechanical properties of the material.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMeanwhile, the physics-informed loss showed a steady decrease from 0.00723 at epoch 0 to 0.00214 by epoch 4500. This is a sign that the addition of physical constraints, i.e., the stress-strain response of the material, was instrumental in guiding the model towards better predictive capability. The physics loss acts as a regularizer, stopping overfitting and making sure the prediction made by the model is not solely data-dependent but also physically realizable.\u003c/p\u003e \u003cp\u003eThe reduction of the total loss from 0.18769 at epoch 0 to 0.03751 at epoch 4500 also indicated that the model was converging to an optimal solution. The coupled loss function, made up of experimental data along with physics-informed terms, managed to combine data-driven model training with physical law preservation. These results demonstrate the capacity of the Advanced PINN model for bridging experimental data with physical laws, augmenting predictive precision with physical consistency in the output.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Evaluation of the PINN-Powered FEA Approach\u003c/h2\u003e \u003cp\u003eThis study's main goal was to improve finite element analysis (FEA) accuracy by including mechanical characteristics that an Advanced Physics-Informed Neural Network (APINN) predicted. Initially, a wide range of experimentally acquired stress-strain responses from 3D-printed PLA specimens with varying raster angles, infill densities, and layer thicknesses were used to train the PINN model. After training, the mechanical characteristics for particular print configurations were predicted by the PINN and utilized as input parameters for the Abaqus FEA simulations.\u003c/p\u003e \u003cp\u003eTo validate the effectiveness of this approach, we tested eight distinct specimens with varying raster angles, layer thicknesses, and infill densities. The mechanical properties predicted by the PINN were utilized in the FEA model, and the simulation results were compared against experimental tensile test data. as shown in Figure.4 The comparison aimed to determine using PINN-enhanced material properties in FEA could yield more accurate predictions aligned with experimental observations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Comparison of FEA Predictions with Experimental Data\u003c/h2\u003e \u003cp\u003eThe stress-strain behavior obtained from the FEA simulations showed a significant improvement in accuracy compared to traditional FEA methods that assume uniform material properties. The incorporation of PINN-predicted mechanical properties enabled the FEA model to capture the anisotropic behavior of 3D-printed PLA specimens more effectively.\u003c/p\u003e \u003cp\u003eTable.1 below summarizes the predicted strain and stress values from FEA compared to the experimentally measured values:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ecomparison table along with error calculations (Absolute Error for Strain and Stress)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRaster Angle (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLayer Thickness (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInfill (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFEA Predicted Strain\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eExperimental Strain\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAbsolute Error (Strain)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eFEA Predicted Stress (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eExperimental Stress (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eAbsolute Error (Stress)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd 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\u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.8320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.8565\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0245\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e36.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e35.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u0026plusmn;\u0026thinsp;45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.5610\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.5236\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0374\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e36.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e36.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.7928\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.7821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0107\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e34.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e34.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.6705\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.6321\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0384\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e35.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e35.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.6634\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.6205\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0429\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e35.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e35.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.1508\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.1371\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e33.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e33.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eKey Observations:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe absolute errors for strain and stress are relatively small, demonstrating the accuracy of the PINN model.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe largest deviation occurs at Raster Angle\u0026thinsp;\u0026plusmn;\u0026thinsp;45\u0026deg; and 0\u0026deg;, which might be due to anisotropic effects in the printed material.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e90\u0026deg; raster angle shows the smallest errors, indicating the model's better predictive accuracy for this configuration.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe error metrics for the strain and stress data\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMetric\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStrain\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStress\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0324\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4963\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0351\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5965\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.9766\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7037\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe values in Table.2 represents the precision of the PINN-based FEA simulation in determining the mechanical properties of PLA 3dprinted specimens. The small Mean Absolute Error for strain (0.0324) indicates that the predicted value for strain closely coincides with the experimental results with minimal deviation. Likewise, the accuracy of the model is once more demonstrated by the low Root Mean Square Error value for strain (0.0351). Strong agreement between predicted and experimental values is revealed by the high R2 value for strain (0.9766), confirming the model's applicability in simulating strain behavior. Although the R\u0026sup2; value for stress (0.7037) is less, indicating some fluctuation in stress predictions, overall agreement remains strong. More importantly, the variation between FEA-predicted and experimental stress values was within an acceptable range, supporting the effectiveness of this approach. These findings highlight the model's capability as well as suggest areas for further improvement, particularly in stress prediction.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn order to increase the prediction\u0026rsquo;s precision of the stress-strain behavior for 3dprinted PLA specimens, this study effectively integrated Finite Element Analysis (FEA) with an advanced Physics-Informed Neural Network (PINN). By training the PINN on actual experimental data the model was able to capture how 3D-printed materials exhibit anisotropic behavior across different printing conditions such as raster angles, layer thicknesses and infill densities. The use of PINN to predict strain and stress behavior, based on print configurations (raster angles, layer thicknesses, and infill densities),as abaqus material property input, the predictive capabilities of the FEA simulation is significantly improved .The PINN-predicted properties were incorporated into Abaqus simulations and compared against experimental tensile test data, revealing a high degree of agreement between the two. The key benefits of this approach are:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003ePINN-enhanced FEA simulations showed noticeably better agreement with experimental data when compared to conventional FEA techniques that assume average material characteristics.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eBy training the PINN model on varied datasets that capture the anisotropic nature of 3D-printed PLA, the predicted mechanical properties more accurately reflect the behavior of specimens under tensile loading.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThis approach allows for the estimation of stress-strain behavior of 3Dprinted objects, across different printing configurations without requiring new experimental testing, which saves both time and resources.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe method works across multiple 3D printing parameters which makes it highly adaptable for use in design and production operations.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThe results state that the integration of FEA with PINN is a solution with a lot of potential and is a good method for doing simulations and predictions of 3D printed parts. This method can be applied to a more detailed, efficient, and reliable simulation in the additive manufacturing. Also, other studies are possible to be conducted that will try this approach on other materials and shapes or to use machine learning in order to refine the material property prediction.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eM.H. Zahmatkeshan conducted the research, performed the simulations, analyzed the results, and wrote the main manuscript text. Associate Professor. F.R.Biglari and Professor B. Mollaei Dariani served as the primary and secondary supervisors, respectively, providing guidance and critical revisions throughout the research process. All authors reviewed and approved the final manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data that support the findings of this study, including simulation results and experimental test data, are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eLokesh, N., Praveena, B. A., Reddy, J. S., Vasu, V. K., \u0026amp; Vijaykumar, S. (2022). Evaluation on effect of printing process parameter through Taguchi approach on mechanical properties of 3D printed PLA specimens using FDM at constant printing temperature. \u003cem\u003eMaterials today: proceedings\u003c/em\u003e, \u003cem\u003e52\u003c/em\u003e, 1288-1293.\u003c/li\u003e\n\u003cli\u003eLeite, M., Fernandes, J., Deus, A. M., Reis, L., \u0026amp; Vaz, M. F. (2018). 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A novel discretized physics-informed neural network model applied to the Navier\u0026ndash;Stokes equations. \u003cem\u003ePhysica Scripta\u003c/em\u003e, \u003cem\u003e99\u003c/em\u003e(7), 076016.\u003c/li\u003e\n\u003cli\u003eInternational Organization for Standardization. \u0026quot;ISO 527-1:2019 \u0026ndash; Plastics: Determination of tensile properties \u0026ndash; Part 1: General principles.\u0026quot; ISO (2019).\u003c/li\u003e\n\u003cli\u003eAadn\u0026oslash;y, B., \u0026amp; Looyeh, R. (2011). Theory of elasticity. In B. Aadn\u0026oslash;y \u0026amp; R. Looyeh (Eds.), \u003cem\u003ePetroleum rock mechanics\u003c/em\u003e (pp. 41\u0026ndash;51). Gulf Professional Publishing. https://doi.org/10.1016/B978-0-12-385546-6.00004-8\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Physics Informed Neural Networks, Finite Element Analysis, Additive manufacturing, Machine learning ","lastPublishedDoi":"10.21203/rs.3.rs-6474572/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6474572/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe accuracy of finite element analysis (FEA) simulations for 3D-printed parts is often limited by assumptions regarding the material's mechanical properties, particularly when these properties are derived from conventional injection-molded specimens rather than directly measured from 3D-printed components. The acquisition of precise mechanical properties for FEA requires testing 3D-printed samples that exactly replicate printing parameters such as raster angle and infill density and layer thickness, which is a time-consuming and expensive procedure. The research presents an advanced technique that improves FEA simulation precision for PLA 3D-printed part tensile strength through Advanced Physics-Informed Neural Networks (PINN). Experimental tensile test data from various raster angles, infill densities, and layer thicknesses enable us to train a PINN for material property prediction which could differ substantially from traditional injection-molded PLA properties. The approach enables the prediction of tensile strength across various printing options while eliminating the requirement for additional physical tests. The research demonstrates that combining PINNs with standard FEA techniques leads to better simulation accuracy and represents a budget-friendly alternative to direct testing. The proposed method demonstrates how machine learning technology speeds up computational methods while addressing the precise modeling challenges of 3D-printed materials.\u003c/p\u003e","manuscriptTitle":"Enhancing Finite Element Simulations of 3D-Printed PLA Using PINN: Validated Through Experimental Testing","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-05 22:11:13","doi":"10.21203/rs.3.rs-6474572/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a023b2b6-0ff4-436b-b20c-b2c0191bc485","owner":[],"postedDate":"May 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-05-19T23:23:11+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-05 22:11:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6474572","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6474572","identity":"rs-6474572","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}