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Abstract

Fused Deposition Modeling (FDM) enables the fabrication of multi-material thermoplastic composites with tailored properties through controlled internal geometries. However, optimizing the trade-off between mechanical properties in PETG–TPU (Polyethylene Terephthalate Glycol and Thermoplastic Polyurethane) composites remains a challenge due to complex parameter interactions. This study investigates the tensile and compressive strength of bioinspired PETG–TPU structures using a surrogate-assisted multi-objective optimization framework. Three architected infill geometries (Octet, Gyroid, and Cross 3D), infill density, and layer thickness were examined. Specimens were fabricated using dual-extrusion 3D printing and characterized via ASTM D638 and ASTM D695 standards. An Artificial Neural Network (ANN) was developed to model nonlinear relationships between printing parameters and mechanical responses, achieving a correlation coefficient (R²) above 0.99 with low prediction errors. The ANN was coupled with a Multi-Objective Genetic Algorithm (MOGA) to identify Pareto-optimal solutions for simultaneous strength maximization. Pareto analysis revealed distinct performance trade-offs relative to architectural configurations. The proposed MOGA–ANN framework provides a computationally efficient approach to optimize architected thermoplastic composites, demonstrating the potential of combining bioinspired design with advanced metaheuristics for high-performance additive manufacturing.

Graphical Abstract

Keywords

Thermoplastic composites bioinspired lattice architectures PETG–TPU hybrid structures artificial neural network (ANN)multi-objective genetic algorithm (MOGA)

Introduction

Thermoplastic composites owing to their recyclability, rapid processing ability, damage tolerance and applicability in lightweight structural applications have gained a sustained attraction from the past few decades.^1,2 In light of these properties, thermoplastic composites are becoming the most suitable choice for aerospace, automotive, biomedical and consumer product industries.³ Polyethylene terephthalate glycol (PETG), is also one such thermoplastic material widely used for its good dimensional stability, chemical resistance, ease of processing and relatively high stiffness compared with commodity polymers.⁴ However, the inherent brittleness and low strain-to-failure ratio of this material made it inappropriate for applications that require high toughness and energy absorption.⁵ Thermoplastic polyurethane (TPU) in contrast to PETG exhibits excellent elasticity, abrasion resistance and energy-dissipation capacity for appropriate structures with a combination of soft and hard segments,⁶ which renders it as one of the best material choices for various applications. TPU’s elastomeric response makes it a suitable choice to ductile and impact-resistant parts. Considering PETG and TPU in a composite or multi-material framework provides an effective approach of maximizing stiffness coupled with toughness. These hybrid composites have the potential for the combined structural properties of PETG, with both strain accommodation and operational crack behavior from TPU. Nonetheless, the mechanical properties of PETG–TPU bi-layers are still very dependent on interfacial adhesion as well as phase distribution, architecture and processing conditions.⁷

Additive Manufacturing (AM) technologies as represented in Figure 1 can be broadly classified according to their respective material deposition processes, which include Vat Photopolymerization (e.g., SLA), Powder Bed Fusion (e.g., SLS), and Material Extrusion (e.g., FDM). Fused Deposition Modeling (FDM) has been identified as a promising technology in the domain of manufacturing due to its potential in processing a wide range of thermoplastic polymers and composites. Although initial investigations on FDM technology involved the use of monolithic polymers, such as PLA and ABS, but recent trends in multimaterial systems, provide a promising opportunity in engineering “soft-rigid” interfaces, which can potentially dissipate energy as in natural structures.^8–11 Significant developments in the use of FDM technology have been reported in the use of functionalized composites, which provide a promising opportunity in enhancing the mechanical and thermal envelopes of the Additively Manufactured structures. For instance, natural fiber composites have been identified as a promising class of composite materials due to their eco-friendly characteristics and high specific strength, thus requiring a critical understanding of the role of constituent properties on the structural integrity of the Additively Manufactured structures.

Figure 1.

An overview of ASTM based classification of additive manufacturing techniques.

Additive manufacturing (AM), particularly fused filament fabrication (FFF),¹² depicts a vast range of multi-material thermoplastic composites with controllable geometrical and architectural features. Since the materials are deposited layer by layer these materials can vary spatially in terms of material distribution, infill geometry and raster orientation which in turn results in tunable mechanical response. However, despite these benefits the properties of FFF manufactured components are often anisotropic, there is limited interlayer adhesion and mechanical properties depend greatly on process factors. In addition, the interfacial character between dissimilar thermoplastics for instance PETG and TPU makes complex load transfer efficiency and propagation behaviour predictions. Therefore, improvement of mechanical properties of PETG–TPU systems manufactured through additive manufacturing depends on a systemic view considering coupling between material combination and both topological and process parameters^13–17

Further, biologically based design principles provide a potential route to tuning mechanical performance in architected materials. Natural materials such as nacre, bones and bamboo exoskeletons have hierarchical arrangements with optimized architecture that provide amazing combinations of stiffness-strength-toughness. The underpinning of their superior performance is based on crack deflection, continuous redistribution of stresses and sliding at the interfaces followed by energy dissipations through controlled heterogeneity. Implementing these principles into engineered thermoplastic composites holds potential for development of both higher damage tolerance and structural efficiency. This approach is typically used in the context of bioinspired architected materials, including microstructured and nanoengineered systems, for which geometric design control and deterministic arrangement of the material are critical to determining mechanical response. Advances in both fundamental understanding, as well as implementation of bioinspired geometries, have demonstrated how principles combined with hierarchical structuring are significant advances towards producing functional and mechanical output performance capabilities from advanced materials systems. However, the cutting-edge strategies belong to multi-material thermoplastic additive manufacturing based on bioinspired architectures have been insufficiently explored (Table 1).

Table 1.

An overview of Comparative Analysis with Existing Literature.

Authors	Architecture/Infill	Material system	Mechanical performance	Optimization/Modeling	Primary contribution	Gap relative to present study
Gibson, Rosen & Stucker (2015)¹⁸	Conventional infill	General polymers	General mechanical behaviour	None	The study lay down the foundational understanding of FDM process–property relations	Lack of bioinspired architecture and optimization framework
Ahn et al. (2002)¹⁹	Raster-based	ABS (FDM)	Tensile anisotropy	Experimental	The study examine the anisotropic strength in FDM	Single material; no 3D infill comparison; no AI driven optimization
Chacón et al. (2017)²⁰	Rectilinear	PLA (FDM)	Tensile strength	Parametric	The study examined the effect of infill density and layer thickness	Lack of multi-material system and evolutionary optimization
Al-Ketan & Abu Al-Rub (2019)²¹, advanced engineering materials	TPMS structures	Architected polymers	Compressive strength	Analytical + experimental	The study evaluated the mechanical efficiency of TPMS lattices	Not focused on FFF PETG–TPU; no GA–ANN coupling
Ngo et al. (2018)²², composites part B	General infill	AM polymers & metals	General mechanical behaviour	Review	The study demonstrates a general review of AM process–structure–property	Lack optimization integration
Guessasma et al. (2019)²³, polymer testing	Various infill types	PLA	Tensile strength	Experimental	Influence of infill architecture on strength	Lack multi-objective optimization
Sood, Ohdar & Mahapatra (2010)²⁴, materials & design	Standard infill	ABS (FDM)	Tensile strength	Response surface methodology	Statistical modeling of FDM parameters	Single-objective; no ANN–GA hybrid
Zhang et al. (2020)²⁵, additive manufacturing	Lattice/TPMS	Polymer AM	Mechanical prediction	ANN modeling	ANN-based mechanical property prediction	No multi-objective GA integration

Considering all abovementioned aspects, the objective of this study is to propose a structured framework which integrates bioinspired architectural design with metaheuristic optimisation approaches for improving mechanical performance of additively manufactured PETG–TPU thermoplastic composites. This research aims toward a most profitable interaction between tensile and compressive strength through an architectural arrangement in conjunction with an multiobjective algorithmic optimisation of the significant processing parameters that can reduce stress concentration and consequently improve mechanical response.^26–28 This work makes contributions to the fundamental science of thermoplastic composites as a systemic approach, based on complementary bioinspirational structural innovations, additive manufacturing specifications and computational optimization strategies connected in one process–structure–property framework. This combinatorial approach sheds light on opportunities for using bioinspired design principles and metaheuristic algorithms simultaneously to guide the design of mechanical performance from multi-material thermoplastic systems generated by additive manufacturing. Such results, which are can provide rational design strategies for next-generation thermoplastic composites with improved structural performance. Figure 2 represents the adapted methodology for proposed research.

Figure 2.

An overview of the proposed methodology used for optimizing PETG-TPU composites for improved mechanical performance.

Materials and Methods

The primary materials used in this study are filament of polyethylene terephthalate glycol (PETG) and thermoplastic polyurethane (TPU 98A). The nominal diameter is about 2.85 ± 0.05 mm. PETG was used for its good stiffness, dimensional stability, and chemical resistance, while TPU 98A was chosen for its elastomeric behavior, strain-to-failure, and energy absorption properties. Figure 2 depicts the proposed methodology used for optimizing PETG-TPU composites for improved mechanical performance. This combination of two thermoplastics offers the possibility for hybrid architectures aimed at enhanced strength–toughness compromise. To avoid moisture-induced defects and to guarantee similar extrusion behaviour, all filaments, stored under the controlled conditions (relative humidity: <50%) of a laboratory at least for 4 weeks before printing. Further, in several experimental runs, the layer thickness (up to 0.6 mm) exceeded the nominal nozzle diameter (0.4 mm). This parameter choice was cautious to induce lateral bead spreading and increase the effective contact area at the PETG–TPU interfaces. By promoting a high-flow extrusion environment, the semi-molten filaments are forced to fill the interstices of the bioinspired lattice more effectively, enhancing the mechanical interlocking between the stiff and compliant phases. This approach effectively reduces the total number of fusion boundaries, which are often the initiation points for structural failure in multi-material additive manufacturing.

BCN3D Stratos is the slicing software used to generate the G-code file. Commercially available3D printer (BCN3D Sigma D25) as represented in Figure 3 was used for fabricating the test specimens. Based upon the fused filament fabrication technology, the printer adopts an Independent Dual Extruder (IDEX) architecture for accurate multi-material deposition. The Bondtech™ dual high-precision extruders and e3D™ hot ends on the system are guided by load cell feedback to ensure precision for close to ongoing production runs with a 420 mm × 300 mm × 200 build volume. A 0.4 mm brass nozzle (default configuration) was utilized for deposition of both PETG and TPU. The machine has a positioning resolution of 1.25 µm in the X and Y axes and 1 µm in Z. Extruder maximum temperature is 300°C while the heated bed can reach up to 80°C with a silicone thermal pad. Further, BCN3D Cura slicing software was used to prepare the printing files. CAD software was used to create the STL models featuring bioinspired architectures and were exported for slicing. G-code files were sent through SD card or WiFi for printing use. Parametric combination of printing parameters were selected based on preliminary trials and manufacturer recommendations to ensure dimensional accuracy and interlayer bonding. The FDM 3D printer was operated in multimaterial mode to fabricate PETG–TPU composite structures with spatially controlled material distribution.

Figure 3.

FDM 3D printer used for fabricating test specimens.

The rastor angle is kept constant at 45° and temperature for fabricating the test specimens is 235 degree Celsius. The test specimens fabricated in this study were assessed for tensile and compressive strength. The equipment used and ASTM standards of test specimens are tabulated in Table 2.

Table 2.

ASTM standards of test specimens.

S.No	Property	ASTM standard	Name of equipment
1	Tensile strength	ASTM D638 type IV	FIE UNITEK (universal testing machine)
2	Compression strength	ASTM D695	FIE UNITEK (Universal testing machine)

The experimental results for tensile and compression testing for different parametric combinations has been represented in Table 3.

Table 3.

Tensile test & Compression test of fabricated specimens at different parametric combinations.

S.No.	Category	Layer thickness	Infill	Compression strength (MPa)	Tensile strength (MPa)
1	Octet	0.64	27.99	67.583	2.0568
2	Gyroid	0.83	27.58	26.3188	2.3436
3	Cross 3D	0.64	24.49	81.6893	1.8813
4	Octet	0.64	23.75	37.8166	2.3434
5	Cross 3D	0.63	26.34	78.5575	2.054
6	Cross 3D	0.64	24.49	81.6893	1.8813
7	Gyroid	0.82	30	19.4858	2.6973
8	Octet	0.58	28.13	66.1429	2.0792
9	Octet	0.62	28.41	62.8626	2.1296
10	Octet	0.65	24.75	42.6662	2.3009
11	Octet	0.68	28.74	59.2554	2.1851
12	Octet	0.67	29	56.7355	2.2237
13	Octet	0.57	29.39	54.0448	2.2639
14	Octet	0.51	30	51.3241	2.3003
15	Octet	0.72	23.81	38.0882	2.3433
16	Gyroid	0.66	27.87	24.227	2.4232
17	Octet	0.63	24.72	42.4524	2.3039
18	Octet	0.7	28.75	59.1049	2.1874

Bioinspired Infill Architectural Patterns

Internal architecture based on bioinspired principles was introduced for improved mechanical performance. Hierarchically arranged natural structures with mechanical optimization strategies such as gyroid, octet and cross 3D are incorporated to integrate the design principles.²⁰ The layer thickness and infill density between PETG and TPU were parameterized in a way that allowed for systematic variation as part of an optimization procedure. Before slicing, CAD models were created representing these structural configurations. Stretch-dominated deformation behavior and strong 3D lattice structure are demonstrated in Octet infill pattern (Figure 4(a)). Because of this triangulated geometry, this architecture enables efficient load transfer pathways with high stiffness-to-weight ratios. One of the key aspect about octet lattice is that it distributes the applied stress uniformly through the structure, minimizing localised stress. The Cross 3D pattern (Figure 4(b)). Is the category of flexible three-dimensional infill architecture. This allows for higher compliance and energy absorption due to bending dominated deformation mechanisms.^29,30 This architecture was chosen for improving ductility and strain accommodation, especially important for TPU-dominant configurations and bioinspired toughening. The Gyroid topology is a type of triply periodic minimal surface (TPMS)-based architecture with continuous curvature and no sharp junctions. The gyroid provides isotropic mechanical response, continuous load paths, improved stress redistribution and reduced stress concentration (Figure 4(c)). Comprising smooth, periodic surfaces, the gyroid is well-matched for bioinspired structural design due to its similarity with natural cellular structures. Its continuous morphology enables crack deflection and progressive failure mechanisms.

Figure 4.

Representation of bioinspired infill architectural patterns (a) octet, (b) cross 3D (c) gyroid.

Metaheuristic-Based Optimization Framework

In modern manufacturing and engineering practices, metaheuristics and machine learning (ML) can be employed together in solving complex, non-linear problems. Although it is a distinct field, there is a symbiotic relationship between the two. The “brain” is ML and the “strategy” in metaheuristics that works simultaneously. A metaheuristic based optimization algorithm was employed to find best combination of structural and process parameters for maximum mechanical performance. The optimization variables include Infill density, Layer thickness and archtecturial infill pattern.³¹ The objective function was defined as a multivariate, combining iteratively measured mechanical properties (including tensile strength, modulus and elongation at break) achieved for various polymer formulations. A multi-objective optimization framework was implemented to achieve stiffness–toughness trade-off.³² The search mechanism employed by the algorithm iteratively assesses candidate sets of parameters, modifies populations through random selection and replacement strategies until it reaches optimal parameter configurations based on both exploration and exploitation approaches typical of meta-heuristic phenomenon.^33–35 To verify the predicted improvements, experimental validation was done on selected optimal designs.

Equipment Used for Mechanical Testing

Commercially available, FIE Universal Testing Machine (UTM) was used in this study to measure the compression and tensile strength of FDM-printed specimens fabricated as per ASTM standards. FIE Universal Testing Machines (UTMs) is used due to its precise and consistent results as these machines have advanced load cells and control systems. We use a microprocessor-based electromechanical machine with a strain gauge type universal load cell that can hold 25 KN. It can measure loads with an accuracy of ±1% from 2% to 100% of the load cell. Following ASTM standards, a crosshead speed of 1.3 mm/min and a strain rate of about 0.05 per minute were used. Figure 5(a) and (b) represents the tensile and compression testing of FDM printing test specimens respectively.

Figure 5.

An overview of (a) tensile testing, (b) compression testing.

Result and Discussion

A detailed performance analysis during the training process was conducted to assess the ANN model predictive capacity developed in this study. Figure 6 represents various states of ANN model including training, testing and validation. Data used for training, testing and vakidation is in order of 70%, 15% and 15% respectively. The backpropagation algorithm used was Levenberg–Marquardt (LM) and the performance function was MSE. This training strategy was chosen because of its quick convergence properties and its suitability for the relatively medium sized experimental data sets commonly used in materials engineering research. Artificial Neural Network (ANN) was established to correlate nonlinear relationships associated with printing parameters, bioinspired infill architectures and mechanical properties of additively manufactured PETG–TPU thermoplastic composites under tensile and compressive loading scenarios. The training state stabilised quickly and ended in 10 epochs after the validation stopping criteria was reached. Early stopping triggered after 6 validation checks with no improvement in validation performance. This stopping criterion is especially useful for materials modelling, whose corresponding experimental data sets may be quite small, leading to overfitting that can quickly deteriorate predictive power. So training was halted once generalization plateaued, even though the model had already lost its predictive ability on past parameter combinations.³⁶

Figure 6.

ANN model configuration.

The model showed a large reduction in prediction error during training. In particular, the MSE began at 742 and concluded at 0.0904 showing that underlying process–structure–property relations were learned effectively. The gradient at termination was 0.83, which means that the net-landed-into-quasi-stationary regional of the error surface. The damping parameter (μ), governing the interpolation between a nineteenth descent and Gauss–Newton optimization of the Levenberg–Marquardt algorithm, converged to 0.01. This behaviour can occur if the solution moves into a region where the domain of second order refinement, or convergence stability lies in larger iteration spaces without oscillatory divergence. Randomly splitting of data in training and validation datasets helps to reduce the distributional bias in model training and promotes better generalization. The Result of training clearly indicates the accomplishment of validation criteria, which states that ANN is successfully trained and model reaches convergence without overfitting. This is critical in this study since mechanical performance depends on strongly coupled and nonlinear relationships between the components of infill architecture (Octet, Cross 3D and Gyroid), infill density, and layer thickness.

The trained ANN was finally coupled into the surrogate model in MOGA framework. To reduce computational resource allocation, both the evaluation of expensive calculations and experiment work were adopted only one time during optimization iterations by using tensile and compressive strengths predicted from a ANN as fitness functions instead in MOGA. By integrating ANN with evolutionary search, high dimensional design space of additively manufactured PETG-TPU composites could be explored in an efficient way while preserving reliable predictive performance. In particular, the ANN successfully recognized different mechanical patterns associated with various bioinspired designs. The predictions of the trained model reproduced the stretch-dominated deformation response characteristic of the Octet lattice, the bending-dominated compliance observed in Cross 3D structures and continuous stress redistribution existing in Gyroid topologies. This confirms the fact that the trained network generated architecture-dependent mechanical responses instead of just fitting global trends. In general, the performance on training reaffirms that the surrogate-assisted optimization strategy is robust. We establish the coupling of Levenberg–Marquardt-trained ANN and MOGA as a dependable computational framework for optimizing tensile and compressive performance characteristics of bioinspired PETG–TPU thermoplastic composites fabricated using fused filament fabrication. All the convergence behaviors, low prediction error results and successful validation proved that the developed MOGA–ANN model is capable of capturing those nonlinear process–structure–property relationships highly relevant in architected thermoplastic composite design.

The regression plots shown in Figure 7 for the ANN model demonstrates that there is a effective linear correlation between calculating mechanical properties experimentally (targets) and ANN predicted outputs for tensile and compressive responses. This includes performance metrics for training, validation and testing datasets and overall regressive analysis. On the training data, the correlation coefficient R = 0.99796. Excellent agreement between predicted and experimental values is observed at high (ideal line: Y = T) as well, evidenced by the fitted regression line being tightly constrained to the ideal line (The regression equation 0.96 × Target +0.57 ≈ Output suggests that there is a slight underestimation tendency for the higher values of target as compared to output, but this is small.). The almost unity slope and the very high R value evidence that the network was able to learn successfully the nonlinear mapping of input parameters (infill architecture, density, material ratio, etc) at mechanical performance.

Figure 7.

Regressions employing artificial neural networks.

The correlation coefficient (R = 0.99926) on the validation dataset also indicates exceptional generalization ability. The regression line (Output ≈1 ∗ Target −0.075) is almost indiscernible from ideal → Y = T; hence, practically no systemic bias. These findings confirm that any signs of overfitting has been properly avoided by the use of appropriate early stopping criteria, and that model is still realistically predictive for input configurations outside the training design space. The same R = 0.99858 for the testing dataset also signifies robust model performance. But while the slope of the regression equation (Output ≈1.2 × Target −2.1) is just over unity, it actually deviates so little that one might expect this minuscule deviation to be acceptable in terms of predictive error for materials modeling studies. The high correlation demonstrates that the ANN captures architecture-dependent mechanical behaviour in separate test samples. Overall regression coefficient: R = 0.9961 when aggregating all data points, demonstrates robust global predictive accuracy across the entire dataset. With the Fitted Output, the regression line overlaps with the ideal prediction line that indicates nearly zero mean systematic bias and stability of model has slope close to unity. Indeed, these regression results confirm the capability of our ANN to capture the complex, nonlinear interactions at play that drive tensile and compressive performance in poorly understood biomimetic PETG–TPU composites on a materials science level. The surrogate model faithfully captures the unique mechanical contributions characterizing Octet (stretch-dominated), Cross 3D (bending-dominated) and Gyroid (TPMS derived continuous curvature) architectures. Such excellent agreement across training, validation and testing sets indicates that the ANN does not simply locally interpolate but is indeed able to generalize within the parameter range considered here.

The R values (0.996) indicate that the trained ANN was reliable and could therefore be included in the Multi-Objective Genetic Algorithm approach proposed here. This keeps the predictive precision wide sufficient in cases that the Pareto-optimal options given by MOGA might depend on actual surrogate assessments, allowing for further computational and experimental cost savings without compromising optimization integrity. Therefore, the regression analysis concludes that constitutive MOGA-ANN model provides consistent and statistically reliable prediction of tensile and compressive properties of constructively manufactured bioinspired PETG–TPU thermoplastic composites.

Classifying the forecasting errors and adding them to a histogram (Figure 8(a)), this research compares how the ANN model behaves with respect to prediction error in various regions using an error histogram.²⁸ The equation (i) given below represents the error:

Target - O u t p u t = Error

(1)

Figure 8.

(a) histogram error plot and (b) plot of mean square error.

Here, the target is experimental tensile or compressive strength and output represents ANN predicted value. The histogram, created from 20 bins, indicates most prediction errors are oriented around zero. The clustering near the zero-error line shows that there is a good match between experimental and predicted mechanical properties. The mean-centered peak around zero indicates no systematic bias of overprediction or underprediction in the model.

Most training data points (blue bars) clusters in a narrow error range roughly between −1 and +1 (in the respective mechanical property units). The validation (green) and testing (red) datasets follow a similar distribution pattern, verifying that the predictive behavior for independent data subsets is consistent. The symmetrical shape of the histogram around zero also proves that the ANN errors are randomly structured and not progressively biased. While there are some isolated points at higher magnitudes of error (i.e. greater than +-3) their occurrence is low. Such deviations are anticipated in experimental materials data because inherent variability from additively manufactured thermoplastic composites, and the impact of architecture-dependent deformation mechanisms (stretch-dominated Octet, bending-dominated Cross 3D, and continuous-curvature Gyroid) on failure behavior. Importantly, these outliers are not part of any systematic trend and thus not indicative of instability of the models. The thick relatively narrow band of errors further validates that the trained ANN captures the nonlinear process–structure–property relationships governing tensile and compressive responses. Mechanical behavior of additively manufactured PETG–TPU systems is a product of several interacting effects including infill density and material distribution. The histogram depicts how well this surrogate model can mimic those interactions with very little variance.

The compression of the error distribution reinforces that the ANN could act as a surrogate in the Multi-Objective Genetic Algorithm (MOGA) from an optimization standpoint. Since the MOGA generates Pareto-optimal solutions through extensive surrogate evaluations, and hence low symmetrically distributed prediction errors are needed for an assured convergence to optimal design configurations.²⁹ Indeed, the error histogram presents evidences of the high predictive power of ANN in all datasets as well as a low degree of bias and stability between generalization performances in this way both training, validation and testing data sets. Insights from this work also reinforce the confirming the integrated MOGA–ANN framework as an efficient optimization strategy for tensile and compressive performance in bioinspired PETG–TPU thermoplastic composites created via fused filament fabrication. The MOGA-ANN utilized a population size of 50, 100 generations, a crossover probability of 0.8, and a mutation rate of 0.01.

Best validation performance curve of ANN in the MOGA–ANN optimization framework is illustrated in this Figure 8(b). MSE constant (Mean Squared Error) versus the number of training epochs, for training and validation testing sets. This analysis is crucial to assess the learning behavior and generalization ability of ANN model developed in this work, which is used for predicting the mechanical performance of additively manufactured PETG–TPU bioinspired composites. Training epochs lies on the horizontal axis and, and Mean Squared Error (MSE) on the vertical axis. The plot shows three curves; the training error (blue line), validation error (green line) and testing error (red line). And the training curve is how well the neural networks fit of the training data during learning. The validation curve is used to track the generalization performance of the model on unseen data, and the test curve gives an independent measure(r) of predictive accuracy after training.

At the start of the training as represented in Figure 8(b), MSE values are approximately at a similar high level for all three datasets as expected because in this early stage of the training, no such underlying relationships between input parameters and mechanical responses have been learnt by the network. As the number of epochs increases, the training error decreases sharply (∼10−3), demonstrating that the ANN gradually learns to map a nonlinear relationship between printing parameters and bioinspired architectures with their respective mechanical properties. The validation error also shows a similar decreasing trend in the first epochs, suggesting that the model is learning better to predict unknown data. The best validation performance is observed in epoch-4 corresponding to minimum value-MSE of 2.1339. The point highlighted in the figure is the optimal trade-off between model fit and generalization. The validation error starts to rise a bit after this epoch, which signifies the start of over fitting. It happens by that the model memorizes the training set instead of learning meaningful generalizations. The training algorithm uses early stopping to avoid this situation, which stops the training process when validation performance is no longer increasing.

The training error continues to decrease even after epoch 4, while validation and test errors only stabilize or grow a bit. The gap between these two lines, or the difference in initial slope of both curves is a classic sign that the model reached its optimal learning capacity for the available dataset. Thus, the network parameters at epoch 4 are final selected to be the trained model. The decreasing error trend indicates that the ANN has successfully learned the complex process–structure–property relationship that controls the PETG–TPU composite structures tensile and compressive behaviour, from a materials engineering point of view. These relations emerge as a result of the interaction between numerous design variables such as infill architecture (Octet, Cross 3D and Gyroid), infill density and material distribution incorporating an additively manufactured structure. Hence, the performance plot shows the ANN model converge steadily with a low degree of prediction error and generalization ability. The best validation performance (at epoch 4) confirmed the trained ANN as a reliable predictor which was integrated into the Multi-Objective Genetic Algorithm (MOGA) framework to find Pareto-optimal solutions for maximizing tensile and compressive strengths of the bioinspired thermoplastic composite structures.

Figure 9 shows the Pareto front calculated using the Multi-Objective Genetic Algorithm (MOGA) applied to the Artificial Neural Network (ANN) surrogate model. The solutions obtained from our optimization analyses are visualized in the Pareto front demonstrating the achievable location between conflicting objectives which differentiate this study i.e., Tensile Strength [MPa] and Compressive strength [MPa] of additively manufactured PETG–TPU Bioinspired Composites. Generally, in multi-objective optimization problems, one can be improved only at the cost of another. This behaviour is evident in the plot, which has compressive strength on the horizontal axis and tensile strength on the vertical one. Each red point represents a valid candidate solution generated from the MOGA throughout the optimization process. The combination of these points constitute the Pareto optimal front, which is a set of solutions where it is not possible to improve tensile strength without making compressive strength worse (and vice versa).

Figure 9.

MOGA-ANN Pareto plot.

A Pareto point distribution shows that the two mechanical responses are inversely related. The high tensile strength predicted is at low compressive strength values relative to each other. For example, the extreme entry at (Compression ≈19.49, Tensile ≈2.70) equates to a configuration with tensile strength although weakest for compression. Conversely, the far-right extreme point in (Compression≈81.69, Tensile≈1.88) (Compression ≈81.69, Tensile ≈1.88) depicts a configuration that exhibits an extremely high compressive strength but low tensile instance. These two points are known as boundary solutions of the optimization space. The intermediate points of the Pareto frontier represent designs with balanced tensile and compressive properties at moderate levels. Alternative formulations are particularly useful for engineering applications in which stiffness and load-carrying capacity have to be compromised. These trade-offs arise from different deformation mechanisms driven by unique internal architectures in bioinspired PETG–TPU composites produced using fused filament fabrication like Octet, Cross 3D and Gyroid configurations. Stretch dominated architectures are gratified by the tensile response of structures, while closer load-bearing arrangements maximise compressive resistance.

The resulting Pareto front provides a decision-making reference to select optimal combinations of such printing parameters and internal architectures based on the desired mechanical performance. Hence, given application requirements (e.g., tensile strength for flexible load-bearing structures or compressive strength to structural support applications), designers can choose solutions along the Pareto curve accordingly. Thus, the Pareto analysis indicates a successful high-dimensional design space exploration for additively manufactured PETG–TPU composites with regards to MOGA-ANN optimization framework implementation. The method provides a set of trade-off solutions instead of a single optimum solution, thus gaining insight into the trade-offs governing tensile and compressive behavior for bioinspired thermoplastic composite structures.

Conclusion

The study was able to successfully demonstrate a surrogate-assisted multi-objective optimization paradigm for the tailoring of the mechanical properties of bioinspired PETG-TPU thermoplastic composite materials. The non-linear interactions of infill patterns and printing conditions were successfully addressed through the integration of Artificial Neural Networks (ANN) and a Multi-Objective Genetic Algorithm (MOGA), yielding a set of robust Pareto optimal solutions to the simultaneous maximization of tensile and compressive strengths. The study made a significant contribution to the multi-material FDM printing, providing a highly efficient computational framework to overcome the limitations of trial and error approaches to material tailoring in FDM. The study also provided a significant breakthrough in understanding the “soft-rigid” mechanical synergies that can be achieved through the digital design of bioinspired lattice geometries, including the Octet, Gyroid, and Cross 3D infills, to produce desired mechanical properties. The high correlation of the proposed ANN model, where R² > 0.99, validates the proposed surrogate modeling paradigm as a reliable solution to addressing multi-objective optimization problems. These results have practical applications in industries where lightweight, energy-dissipating structures are necessary. This ability to forecast and optimize the performance of a soft-rigid interface can be used to develop materials that are “programmable” to specific needs. This can be accomplished without complex manufacturing schemes. Through the use of the MOGA–ANN methodology, a significant reduction in experimental runs was achieved. This resulted in a more environmentally friendly process in terms of minimizing waste materials and energy consumption during the R&D phase. Also, as a result of selection among PETG and TPU, which are recyclable materials, a more sustainable future in manufacturing can be achieved by utilizing eco-friendly, high-performance materials such as composite materials. Future research directions should be aimed at understanding more about the micro-structural properties of PETG/TPU through SEM and Nano-indentation. Also, a deeper understanding about environmental factors such as aging effects and moisture absorption on bio-inspired materials will be necessary.

Footnotes

Acknowledgements

Authors sincerely acknowledge SGT University for providing laboratory facilities and UIET, M.D.U for providing testing facilities.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the author(s) used AI assistance to improve the readability and language of the manuscript. The authors reviewed and edited the final content and take full responsibility for the content of the published article.

ORCID iD

Ashish Kaushik

Data Availability Statement

Data will be made available on request.*

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Bioinspired design and metaheuristic driven process optimization of FDM printed PETG–TPU thermoplastic composites for improved mechanical performance

Abstract

Keywords

Introduction

Materials and Methods

Bioinspired Infill Architectural Patterns

Metaheuristic-Based Optimization Framework

Equipment Used for Mechanical Testing

Result and Discussion

Conclusion

Footnotes

Acknowledgements

Declaration of Conflicting Interests

Funding

Declaration of generative AI and AI-assisted technologies in the writing process

ORCID iD

Data Availability Statement

References