Optimization of mechanical performance in bioinspired FDM-printed PLA sandwich structures using machine learning

Abstract

Despite some successes and claims of the best possible mechanical performance in 3D printed parts, it is essential that intelligent design approaches be linked to intelligent process control. In this paper, an integrated experimental-machine learning methodology is presented to optimize the polylactic acid (PLA) sandwich structures that has bio-inspired internal cores. They are made using Fused deposition modeling (FDM). Six basic geometries AS, ASR, ASVC, HAR, HAS and HASV were printed with three orientations 0⁰, 45⁰ and 90⁰ to have 54 specimens. Mechanical properties, including maximum load, ultimate tensile strength, Young’s modulus, tensile stress at break, and tensile strain, were measured and studied with the help of the Taguchi method and ANOVA, which held core structure and raster orientation as having significant effect. The HASV core with 0⁰ raster orientation reached the maximum load value of 1426.3 N, maximum UTS value of 18.3 MPa, and Young’s modulus value of 933.7 MPa, which is 168% stronger than the weakest configuration (HAS, 45⁰, 532 N). ASR at 0° exhibited the greatest ductility (tensile strain 12.79%). The ANN model with the usage of Bayesian Regularization (10 neurons) provided a training R = 0.975 and the mean 5-fold-cross validation R = 0.962, proving a good predictive ability of the model without overfitting. These results offer an effective way forward to the design of PLA parts facing high loads, proving that statistical optimization, combined with AI, is the way forward in the field of additive manufacturing.

Introduction

The concept of additive manufacturing (AM) has changed the design and manufacturing paradigm of various engineering uses, providing capabilities that no other production method can provide due to the lucrative freedom and flexibility of design. Out of all AM technologies, Fused deposition modeling (FDM) is most often accepted in its mass use because of affordability, availability, and suitability with the combination of thermoplastic material^1,2. Polylactic acid (PLA) has been used as an ideal material in FDM as it has a biodegradability feature to it, that is, its sufficient mechanical performance and convenience of processing^3,4. According to Wang et al., (2023) FDM technology allows complex geometries to be manufactured in a layer wise manner, automatically building on 3D computer-aided design (CAD) data and introduces new lightweight and high-performance opportunities in structures⁵.

The mechanical properties of the printed PLA parts significantly depend on an array of process parameters such as the height of the layers, speed of printing, the angle of the raster, the orientation of the build and the internal structure construction. Mengesha Medibew (2022) noted that despite the apparent benefits of FDM process, one of the inherent drawbacks to its professional enterprise adoption is the insufficiency of stronger mechanical properties, the properties of the manufactured product by FDM are severely contingent upon the selection of FDM parameters⁶. This parameter sensitivity poses challenges/opportunities to part performance optimisation with regard to a particular application. Recent investigations have shown that the strategic choice of FDM process parameters such as the layer height, the print speed and the raster angle can substantially enhance the tensile strength, surface finish and the efficiency of production of printed PLA components⁷.

Although the Taguchi method has been popular in 3D printing studies because it is efficient in experimental purposes and optimal power to exert on parameters it intends to optimize^8–10, this technique requires a systematic approach to multi-parameter optimization. Sharma et al. (2021) also highlight the fact that Taguchi approach to plan an experiment is a unique and powerful method of experimental analysis and product, process optimization, etc¹¹. When orthogonal arrays and signal-to noise (S/N) ratio analysis is used, researchers will be able to narrow their combinations of parameters by selecting the best ones and reducing the number of experiments to run. This has been found especially useful in the optimization of FDM processes where parameter interactions are so complex such that one-factor-at-a-time experiments are inefficient and ineffective. Moreover, ANOVA is used in most cases to be able to give a statistical proof of the significance of factors.

Artificial Neural Networks (ANNs) are the computer-based computational systems which are designed by taking inspiration of brain that is consisted of an input layer, one or more hidden layers, and an output layer in which there are interconnected neurons that process weighted inputs with the help of nonlinear activation functions as Tan-Sigmoid or hyperbolic tangent to generate outputs^12,13. During the training, the prediction errors are incrementally back propagated to modify connection weights to reduce the total error^13,14. The Levenberg-Marquardt algorithm works most well on small to medium-size data sets because of its rapid convergence^12,15, whereas the Bayesian Regularization helps to avoid overfitting by automatically penalizing the model complexity-and is thus most useful for controlled through limitless data from experiments^14,15. These capabilities have been verified on a wide range of engineering material prediction problems^12–16.

In additive manufacturing, artificial neural networks (ANNs) have shown great predictive power as the modeling of process-property relationships in fused deposition modeling (FDM)^17,18. Inayathullah et al. (2025) reviewed machine learning applications in additive manufacturing and brought out that Taguchi-ANN hybrid frameworks can obtain high predictive accuracy for process parameter optimization¹⁹. Subramanian et al. (2023) predicted yield stress, Young’s modulus, UTS, flexural strength and elongation of FDM components using machine learning models with prediction errors less than 10%²⁰, while several studies have reported R2 values more than 0.94 for prediction of tensile strength of PLA components^21,22. In a context of high-performance FDM polymers, Borah et al. (2025)²³ developed machine learning models to predict roughness, tensile strength and elastic modulus of FDM-printed PEEK components with prediction deviations below 4%. Related studies on the same material system have discussed alternative ways of regression including support vector regression and random forest regression²⁴, and ridge and Bayesian regression models²⁵, which prove the effectiveness of machine learning methods for predicting mechanical properties of additively manufactured polymers. Furthermore, hybrid optimization schemes combining Grey Relational Analysis, ANFIS and genetic algorithms have been proposed for multi-response optimization of FDM process parameters²⁶ and such data-driven optimization schemes have been applied in other manufacturing areas such as MQL machining of Ti6Al4V alloy²⁷, illustrating wider use of machine learning optimization schemes in advanced manufacturing. Building on this, the current study has used an ANN using Bayesian Regularization, 10 hidden neurons and 5-fold cross validation to predict 5 mechanical properties of FDM-printed PLA sandwich structures with 6 bio-inspired core geometries and 3 raster orientations.

Although there has been a considerable improvement in the field of optimization of FDM parameters, it is remarkable that, there lacks a proper literature on systematic study of internal core structures and their correlation with the process parameters. Studies have previously concentrated mostly on conventional infill patterns (honeycomb, triangular, rectilinear) and less attention has been given to new core geometries that may result in good mechanical performance and at the same time retain the lightweight properties^28–30. According to Caran et al. (2023), an alternative new core structure is being presented to the commonly used honeycomb and square core structure in the literature. The designed structure had the highest compressive strength of 9.867 MPa which is 32.18% and 54.36% more than the honeycomb and square core structure³¹. Jackson et al. 2022 have shown how multi-parameter optimization procedures, e.g. Taguchi method can be used to greatly improve the mechanical quality and surface features of FDM-printed PLA components by assessing the impact of process parameters e.g. layer height, print speed, infill density, etc., in a systematic manner⁷.

To the best of the authors knowledge, no previous investigation has been carried out simultaneously to investigate 6 bio-inspired auxetic core structures based on the structure of the pistachio shells’ microstructure, optimizing their tensile performance by Taguchi L18 mixed orthogonal array with the combination of ANOVA and a Bayesian-Regularized ANN, which is trained on bio-inspired datasets for mechanical property prediction. This integrated approach is the main novelty introduced in the present work. The paper is a descriptive study of mechanical characteristics which assesses 3D printed polylactic acid (PLA) samples using six different core structures (AS, ASR, ASVC, HAR, HAS, HASV) and studied at different raster orientation (0°, 45°, 90°). Through incorporation of Taguchi, ANOVA, and ANN, the study would help in optimization of the process parameters, and thus, will fill a significant knowledge gap on the effect of the core geometry and the print direction on tensile performance. Towards this aim, the paper frames the following research questions.

1. What are the effects of other bio-inspired core structures on the tensile mechanical properties (maximum-load, ultimate- tensile strength, young’s modulus, tensile-stress and tensile-strain-at-break) of 3D-printed PLA samples?

2. What are the effects of important print parameters, i.e., layer height, print speed, raster angle, on the mechanical property of the PLA samples of different core geometry types?

3. What are the base structure and printing parameter sets to achieve optimal mechanical properties in FDM- printed PLA parts?

4. Does the Taguchi technique, combined with ANOVA, effectively identify critical factors and optimize process parameters to minimize degradation of the mechanical properties in 3D-printed PLA parts?

5. How far is the Artificial neural network (ANN) model able to predict the mechanical properties of PLA specimens based on the core structure and printing parameters, thereby removing the need to carry out a costly round of experiments?

Materials and methods

Materials

The under-investigation specimens were printed using the JAMG HE High-Speed PLA+ filament (Brand: JAMG HE, Color: White, Diameter: 1.75 mm, Item Weight: 998 g; Fig. 1 (b)). This material was specifically designed to work at high-speed FDM printing and it is recommended that they be printed at 190–240 °C nozzle temperature and 45–60 °C bed temperatures. Specific features are melt flow index of 10.68 g/10 min (190 °C, 2.16 kg) and fluid supply that is tangle-free that facilitates uniform flow and high success rate. The filament will work in high-speed or conventional FDM printers and are known to be stronger, tougher, and with good layer adhesion creating prints with limited warping with a glossy print finish.

Fig. 1.

(a) Pratham 3.0 FDM 3D printer; (b) PLA filament.

3D printing equipment

All the specimens were 3D printed on the Pratham 3.0 FDM printer (Build Volume: 300(W) x 300(D) x 300(H) mm; Layer Resolution: 80–600 μm; Filament Compatibility: PLA, ABS, TPU, PETG, Carbon Fiber composites; Extruder Temperature: up to 280 °C, Bed Temperature: up to 120 °C, Printing Speed: 120–150 mm/s, XY Precision: 11 μm, Z Precision: 10 μm). It has wireless connectivity such as the Wi-Fi, USB, and SD card, and uses a touchscreen of 4.5 inches to control the printer (Fig. 1(a)). The slicing and print preparation endeavors were made in standard slicing software.

Development and fabrication of biomimetic cores

The present work relied on the hierarchical microstructure of pistachio shells whose thick-walled lamellar curvatures interlock and can attain remarkable energy absorption and mechanical strength (Xiao et al., 2021)^32,33. A novel group of augmented lightweight cellular cores was designed by following a biomimetic design methodology. The microstructure of pistachio shell, such as scanning electron microscopy (SEM) images and parameters characterizing the lamellae were obtained by Xu et al. (2014) and Thanikasalam et al. (2024) who made a thorough analysis of the lamellar honeycomb concept and mentioned the natural effectiveness of lamellar structure in stress transfer and energy dissipation^34,35. Driven by these design concepts that are found in nature, it has led to the development of the lightweight biomimetic bi-folding core structures to satisfy the load transfer, dissipation of stresses as well as absorption of energy similar to that used in the shell (Fig. 2).

Fig. 2.

The micro structure of pistachio shell (reproduced from Xu et al.³⁴, Scientific Reports, under CC BY 4.0 license).

Six-unit cell topologies based on the honeycomb were first conceived (Fig. 3)

Fig. 3.

Unit cell topologies.

1. HC (Honeycomb cell): the standard regular hexagon lattice.

2. HCR (Honeycomb cell with rounded corners): a rearrangement which reduces the high stress corners of the regular honeycomb making it more stress free and tougher.

3. HCVC (Honeycomb cell with varying cross Section): It is a variation of honeycomb cells that alter the thickness or height of the wall along its length to locally stiffen regions of high stresses and adding shear strength as well as strength-to-weight ratio.

4. HCL (Honeycomb cell with lamellar curve): It is a geometric variant and is defined by a sinusoidal wall structure of lamellar walls to formalize an optimization approach whose focus is to improve stiffness and energy-absorption.

5. The HCRL (Honeycomb cell with rounded corners and lamellar curve) structure is a combination of the stress releasing ability of rounded corners and structural stiffness by lamellar reinforcement.

6. HCLVC (Honeycomb-lamellar curve with varying cross section) is a new type of an intermediate hybrid construction combining a lamellar reinforcement and the variation of cross-section to induce stepwise changes in stiffness and exhibit greater adaptability under complex loading.

Design advantages that can be expected of these cell types are that they offer smoother load paths inside, reduce stress concentration areas, increase stiffness, crack resistance, control deformation, and energy absorption efficiency. Geometries with rounded corners allow the sharing of stresses in an even manner, lamellar curves enhance the transfer of loading shear, and cross-sections are curved in different ways to allow larger or smaller stiffness for strength without increasing weight. It is important to note that pistachio shells are not intrinsically auxetic, instead, they have a hierarchical lamellar curved architecture that allows stress transfer and energy dissipation. This geometry of a lamellar curved pattern was taken as a biomimetic template and geometrically transformed into re-entrant unit cell configurations. The inward-pointing (re-entrant) geometry of the cell walls induces a negative Poisson’s ratio (NPR) response where the structure expands laterally rather than contracting with tensile loading that is the defining mechanical characteristic to the auxetic behavior.

These six honeycomb-based unit cell topologies (HC–HCLVC) formed the geometric and biomimetic design basis for the subsequent development of six auxetic core structures (Fig. 4) AS (Auxetic structure), ASR (Auxetic structure with rounded edge), ASVC (Auxetic structure with varying cross section), HAS (Hexagonal auxetic structure), HAR (Hexagonal auxetic structure with rounded edge), and HASV (Hexagonal auxetic structure with varying cross section)which were fabricated as physical specimens and subjected to mechanical testing in this study. These geometries were truncated in order to take advantage of negative Poisson effects, to increase shear growth laterally when subjected to a tensile load, and to increase energy absorption and to distribute weight loads^36,37. This bendable and interlocking geometry of these constructs was guided by the unique microstructure of the pistachio shells known to have a large load-bearing contribution as well as large energy absorbency³⁸.

Fig. 4.

Unit cell design of six type of cores.

In order to accurately determine wall thickness, curves and transitional areas, all designs were parametrically modelled in CAD and based on the organic lamellar patterns created by pistachio shells. STL files of the models were exported, sliced and printed under FDM on a Pratham 3.0 printer with commercially bought PLA material. Parameters governing the geometric fidelity, including nozzle temperature (210 °C), bed temperature (50 °C), and infill density (100%), as well as walls count — (3) were standardized for all the specimens for dimensional consistency, whereas the four experimental factors of the Taguchi methods were systematically varied as described in Sect.  2.4.

Specimen design

Tensile test samples, which were used in this study, were made as per ASTM (American society for testing and materials) D638 type I requirements of plastic materials. Specimens had the geometry of dumbbells, with a total length of 165 mm, a gauge-section width of 13 mm, a gauge-section thickness of 3.2 mm and the gauge length of 50 mm. Failure consistently occurred within narrow gauge area which has highest stress concentration for thorough characterization of material properties^39,40.

As shown in Fig. 5, the core ideas that are discussed in the center gauge part of ASTM D638 specimens were substituted with modeled inner structures instead of solid substance. This alteration led to the loss of mass of the specimen, and at the same time preserving or increasing mechanical effectiveness — consistent with the sandwich specimen design approach reported by Dairabayeva et al. (2024)⁴¹. The basic structures were contained within the 50 mm gauge length in a sandwich type structure, with solid end segments, for adequate gripping for tensile test. All the specimens were additively manufactured out of Polylactic Acid (PLA) using FDM 3D printing.

Fig. 5.

Tensile test specimen for a sandwich core structure.

Although the external specimen dimensions are in accordance with the standards for a Type I specimen of the ASTM D638 standard, the use of cellular core structures in place of the solid gauge section is a deliberate geometric change from the normal specimen configuration. This modification was deliberately made in order to explore the role of internal core architecture on the tensile mechanical performance of the printed structures.

Experimental design using Taguchi orthogonal array

A Taguchi L18 Mixed orthogonal array was then chosen to fit one 6 level core structure factor and three 3 level raster angle, layer height and print speed factors resulting in 18 experimental runs. Each run was repeated 3 times to make it statistically reliable, so a total of 54 specimens were obtained. The factor levels are summarized in Table 1. Specimens were fabricated based on the design matrix 54, which involves all the changes in four factors: (1) the core structure type (there are six discrete architectural structures, AS, ASR, ASVC, HAS, HAR, and HASV); (2) the height between the layers (0.10, 0.15, and 0.20 mm); (3) the speed of printing (60, 65, and 70 mm/s); and (4) the raster angle (0⁰, 45⁰, and 90⁰).Despite the overall similarity in the exterior size of the specimens, the parameters led to different internal core geometry of the specimens. This enabled the study of auxetic geometries, shape of the edges (rounded and sharp), and the structure of the cross-section. Taguchi analysis has been done by manually building and allocating factors in the L18 array using conventional procedure. All the experimental data have been tabulated in Table 2 and analyzed in Excel, where the means and signal-to-noise (S/N) ratios were calculated using spreadsheet formulae. The ANOVA was performed using JMP Pro because the factor effects need to be relevant, and the parameter combinations should be maximized using the robust experimental design and the common and open-source software, such as Excel and JMP Pro. The L18 orthogonal array is designed to assess main effects independently from one another and fails to capture two-way interaction effects. Given the observed anisotropic behavior between the raster angle and the geometry of the cores, new research with a full factorial design or Response Surface Methodology (RSM) design would be useful in order to quantify these interaction effects explicitly.

Table 1.

Process parameters and their levels for Taguchi L18 orthogonal array.

Factor	Levels	Values
Core Structure	6	AS, ASR, ASVC, HAS, HAR, HASV
Layer Height (mm)	3	0.10, 0.15, 0.20
Print Speed (mm/s)	3	60, 65, 70
Raster Angle (°)	3	0°, 45°, 90°

Table 2.

Taguchi L18 orthogonal array and parameter combinations.

Run	Core Structure	Layer Height (mm)	Print Speed (mm/s)	Raster Angle (°)
1	AS	0.1	60	0
2	AS	0.1	65	45
3	AS	0.1	70	90
4	ASR	0.15	60	0
5	ASR	0.15	65	45
6	ASR	0.15	70	90
7	ASVC	0.2	60	0
8	ASVC	0.2	65	45
9	ASVC	0.2	70	90
10	HAS	0.1	60	0
11	HAS	0.1	65	45
12	HAS	0.1	70	90
13	HAR	0.15	60	0
14	HAR	0.15	65	45
15	HAR	0.15	70	90
16	HASV	0.2	60	0
17	HASV	0.2	65	45
18	HASV	0.2	70	90

Each experimental run in the Taguchi L18 orthogonal array was replicated three times to ensure statistical reliability, resulting in a total of 54 specimens.

Mechanical testing

Before experimentation, the test specimens (Fig. 6) were accustomed to the ambient laboratory conditions and exposed to a length of time of 24 h. The specimen was then tested under a tensile test conducted following the protocol of ASTM D638 and using the universal testing machines (Fig. 7). The outputs that were measured as follows included the maximum load, ultimate tensile strength (UTS), Young’s modulus, tensile stress and strain at the time of failure. Each experimental condition was repeated three times (n = 3) in order to obtain the repeatability of the measured mechanical properties. This level of replication is consistent with common experimental practice in Taguchi based experimental designs and additive manufacturing studies^8,42,43.

Fig. 6.

Tensile testing specimens.

Fig. 7.

Tensile test setup.

Statistical analysis with ANOVA

In order to examine the origin principal effects and also to identify the best configurations of parameters based on strength-related attributes, the Taguchi experimental design was carried out. The larger the better signal to noise ratio was taken. It was ANOVA through which statistical significance and the individual contributions of each causing factor have been determined, also performed on JMP Pro 18 software. The method of least-squares produced a regression line whose values would minimize the total squared distances between the line and each of the data points. This was used to develop an artificial neural network (ANN) model trained on the experimental inputs variables to predict the mechanical properties, the performance of which was tested with a hold-out test set. Following completion of the ANOVA, Tukey’s Honest Significant Difference (HSD) post-hoc test (alpha = 0.05) was performed in JMP Pro for all statistically significant factors (Core Structure, Raster Angle and Print Speed) to identify specific pairwise factor level differences. Layer height was not considered in post hoc results analysis because no statistically significant difference was found among the five responses (p ≈ 1.0).

ANN prediction

The in-depth study was carried out where the artificial neural networks (ANNs) were applied to predict the mechanical characteristics of 3D-printed PLA samples by the impacts of several core patterns and processing settings. The non-linear nature of a relationship that occurs between the input factors (core type, layer height, print speed, a raster angle) and output variables (maximum load, ultimate tensile strength, young’s modulus, tensile stress at break and tensile strain at break) is well captured through use of Artificial Neural Networks (ANNs).

The ANN was considered with an architecture of 3 layers of 4 inputs, 1 hidden layer with 10 neurons, and 5 outputs (Fig. 8). The categorical variable ‘core structure’ was encoded by means of integer run-index values (1–18) corresponding to the 18 experimental runs of the Taguchi L18 orthogonal array, which represents each index as a unique specific type of core and parameter combination (Table 2). Prior to training, all inputs were automatically normalized to [− 1,1] by using the mapminmax scaling function in MATLAB which eliminated any bias in magnitude introduced by the integer encoding of inputs. The number of hidden neurons has been determined by the following established heuristic rule:

1

Fig. 8.

Neural network fitting tool (nftool).

where N = 54, Inputs = 4, Outputs = 5, and α = 2, recommending approximately 3–6 neurons.

In order to find the best ANN architecture, a sensitivity analysis study was performed by adjusting the number of hidden neurons. Networks of 5, 8, 10, 12 and 15 neurons were tested using 5-fold cross validation with the Bayesian regularization (Fig. 9). The performance comparison is summarized in Table 3. The results indicate that the 10-neuron architecture was able to produce the highest balance between the training accuracy and generalization since the results are Training R = 0.975 and the cross-validation mean R = 0.962 were found to produce the smallest training-validation gap that is estimated to be 0.013. Therefore, a single hidden layer with 10 neurons was selected for the final ANN model.

Fig. 9.

Effect of hidden neuron count on ANN performance showing training R and 5-fold cross-validation R. The 10-neuron architecture is found to have the smallest training-validation gap (0.013), which confirms that it will have optimal generalization ability.

Table 3.

Sensitivity analysis for hidden neuron selection.

Hidden Neurons	Training R	5-fold CV (Mean R)	Gap	Overfitting Risk
5 (Bayesian regularization)	0.941	0.923	0.018	Low
8 (BR)	0.968	0.951	0.017	Low
10 (BR)	0.975	0.962	0.013	Low Selected
12 (BR)	0.976	0.958	0.018	Low–Moderate
15 (BR)	0.978	0.951	0.027	Moderate
50 (Levenberg–Marquardt)	0.9987	0.9596	0.039	Overfitting

To avoid the overfitting problems related to the small size of the training data, Bayesian Regularization (BR) algorithm was used as a training algorithm. Bayesian regularization makes network weights random variables with Gaussian priors: it optimizes with the following regularized objective function:

2

where E_D is the sum of the squared of prediction errors, E_W is the sum of the squared of weights of the network and α, β are hyperparameters for regularization which are optimized automatically by using Bayesian inferences:

3

4

where N = 54 (total specimens) and γ = 77.3 is the effective number of parameters determined by the algorithm — reduced from the 105 nominal parameters [(4 × 10) + (10 × 5) + 10 + 5 = 105]. This automatic complexity penalization removes the requirement of the separated validation set and overfitting without the requirement of manual tuning (Fig. 10). The entire dataset of 54 specimens was used for BR training. To independently verify generalization capability, a 5-fold cross-validation was subsequently performed, where the dataset was partitioned into 5 equal subsets with each subset used once as the test set while the remaining four subsets were used for training. The result is that the model can efficiently and accurately measure mechanical properties of novel combinations of model parameters and hence enables virtual optimization and design in additive manufacturing. In order to obtain a better interpretability of the ANN model, the relative importance of the input variables has been evaluated through the statistical contributions that can be obtained by the use of the analysis of variance.

Fig. 10.

Neural network architecture.

Results

Experimental result

The tensile behavior of all specimens used was initially assessed by using stress-strain and load-strain curves as shown in Fig. 11(a) and (b). Such plots can be used to directly compare strength, stiffness, and ductility between the various core architectures and orientations of the rasters. Table 4 indicates tabulated mechanical properties of PLA tensile specimen 3D-printed by different bio-inspired core structures and raster angles (Fig. 12). The table contains the mean values and their standard deviations (SD) of five important tensile parameters obtained after testing samples in several replicates per each unique combination of core type and raster angle: Maximum Load (N): The maximum load the sample could withstand until failure. Ultimate Tensile Strength (UTS in MPa): The ultimate stress the material is in before letting go. Youngs Modulus (MPa): Strength of the item being tested as determined by the gradient of the stress-strain curve within the elastic range. Tensile Stress (MPa): Stress at a given point at tensile test. Tensile Strain (%): The relative elongation prior to fracture, expressed as a percentage.

Fig. 11.

(a) Load vs. tensile strain. (b) Tensile stress vs. tensile strain.

Table 4.

Mechanical Properties of 3D-Printed PLA Specimens with bio-inspired core structures.

Sample	Core structure (with raster angle)	Maximum Load(N)		UTS(MPa)		Young’s Modulus (MPa)		Tensile stress (MPa)		Tensile strain (%)
		Mean	SD	Mean	SD	Mean	SD	Mean	SD	Mean	SD
1	AS 0	967.1	30.3	12.7	0.6	807.0	0.8	2.5	1.5	10.09	1.64
2	AS 45	703.9	33.8	9.0	0.0	571.8	12.3	3.3	0.4	4.14	0.35
3	AS 90	627.5	17.8	8.0	0.0	607.7	2.8	2.2	0.2	2.85	0.21
4	ASR 0	1044.8	30.6	13.3	0.6	852.6	10.7	1.7	0.3	12.79	0.76
5	ASR 45	857.5	11.3	11.0	0.0	644.6	3.0	5.3	1.3	7.03	0.48
6	ASR 90	744.8	26.5	9.7	0.6	624.4	22.7	2.3	0.5	4.06	0.04
7	ASVC 0	1110.6	89.6	14.0	1.0	869.8	60.1	4.7	0.5	16.01	1.69
8	ASVC 45	848.0	10.3	11.0	0.0	724.8	22.6	4.4	0.2	6.25	0.50
9	ASVC 90	802.5	3.0	10.0	0.0	750.0	10.4	4.8	2.7	3.70	0.33
10	HAR 0	986.2	4.7	13.0	0.0	782.2	19.8	5.5	0.7	9.78	0.89
11	HAR 45	698.8	73.5	9.0	1.0	514.3	50.7	2.8	0.3	5.51	0.42
12	HAR 90	641.7	4.4	8.0	0.0	722.8	33.4	8.2	0.1	1.56	0.20
13	HAS 0	975.5	16.8	12.5	0.5	751.5	9.8	3.0	0.6	8.31	0.68
14	HAS 45	532.0	19.2	7.0	0.0	409.5	16.7	2.7	0.5	4.81	0.96
15	HAS 90	577.4	38.2	7.5	0.5	527.6	2.4	4.7	3.0	3.32	1.12
16	HASV 0	1426.3	43.0	18.3	0.6	933.7	19.2	8.1	1.4	6.59	0.71
17	HASV 45	863.8	13.3	11.0	0.0	730.3	12.1	10.7	0.2	2.24	0.13
18	HASV 90	675.2	66.9	9.0	1.0	691.8	24.0	8.3	0.5	1.54	0.23

Data presented as mean ± standard deviation (n = 3 specimens per group). Total specimens tested: 54.

Fig. 12.

Tensile specimen after testing.

There is significant variance in a comprehensive examination of the mechanical performance produced by 3D-printed parts having different core structure and raster angle. The respective important findings are as follows: The core structure of the HASV printed with a 0⁰ raster angle produced the highest mean maximum load (1426.3 N), elastic strength (18.3 MPa) and rigidity (Young’s modulus of 933.7 MPa) due to the obvious mechanical resilience. Specimens that had AS core and a 0 deg raster had relatively similar maximum loads (967.1 N) and stiffness. An obvious, significant effect is raster angle: parts printed with the direction of filament roughly parallel to the loaded axis often perform significantly better than those printed at 45⁰ or 90⁰ perpendicular to the loaded axis, a demonstration of the benefit of the filament direction. The tensile strain values increase on the average at 0⁰ raster angle on most of the cores indicating bigger ductility. Large standard deviations in some groups (e.g., ASVC core at 0 degree with SD of 89.6 N loading) mean that prints have varying quality or sample consistency. Together, these values offer holistic consideration of the impact of bio-inspired core geometry and raster angle on the tensile mechanical properties of PLA 3D prints to guide optimal design and fabrication conditions to maximize the structure performance.

Taguchi analysis

Calculating Signal-to-Noise (S/N) Ratios

For each unique combination of factors (core, layer height, print speed, raster angle), the Larger-the-Better S/N ratio for Maximum Load is:

5

Where Y_i is each measured maximum load for the condition.

Response tables for Taguchi analysis

Mechanical properties under analysis were determined as S/N ratios. The derived response tables include average values of S/N of each level of factor (core type and orientation), delta (difference between the maximum and minimum S/N) and ranking of factors according to its effect on the properties.

As seen in the analysis of Maximum Load (Table 5), orientation is found to be the most influential, with a higher value of difference (Delta) (4.06) as compared to core type (2.94). Among the core-type, HASV has the biggest signal-to-noise ratio (SNR; 59.44 dB). In comparison to orientation, 0⁰ shows good results everywhere in terms of transitions relative to 45⁰ and 90⁰.

Table 5.

Response table for maximum load.

Level	AS	ASR	ASVC	HAR	HAS	HASV	0°	45°	90°
Mean S/N (dB)	57.52	58.82	59.17	57.61	56.49	59.44	60.61	57.37	56.55
Delta	–	–	–	–	–	2.94	4.06	–	–
Rank	5	3	2	4	6	1	1	2	3

There was a considerable distinction between the influence of core type and orientation at UTS. The greater effect size (Delta = 3.84) was noted in orientation, and the Delta value of core type was 2.95 (Table 6). Smoothly working HASV seemed to work best with the negative S/N ratio of -38.22 dB, and in regards to orientation, 0 angle showed an unquestionably better performance.

Table 6.

Response table for ultimate tensile strength (UTS).

Level	AS	ASR	ASVC	HAR	HAS	HASV	0°	45°	90°
Mean S/N (dB)	− 40.30	− 38.96	− 38.82	− 40.02	− 41.17	− 38.22	− 37.29	− 40.32	− 41.13
Delta	-	-	-	-	-	2.95	3.84	-	-
Rank	5	3	2	4	6	1	1	2	3

In Youngs modulus, core type has an even more than orientation (Delta = 3.11) influence. ASVC shows largest S/N ratio (57.80 dB) which closely appeals to HASV (57.77 dB). The optimum performance can still be achieved through the 0⁰ orientation (Table 7).

Table 7.

Response Table for Young’s modulus.

Level	AS	ASR	ASVC	HAR	HAS	HASV	0°	45°	90°
Mean S/N (dB)	56.34	56.95	57.80	56.32	54.69	57.77	58.38	55.35	56.21
Delta	–	–	3.11	–	–	–	3.03	–	–
Rank	4	3	1	5	6	2	1	3	2

In Tensile Stress at Break, core type is a much stronger factor (Delta = 11.48), in comparison to orientation (Delta = 2.41). The S/N ratio of HASV is 18.64 dB, which is much higher in comparison with other core types. The orientation which performs best on this property is 90⁰ orientation (Table 8).

Table 8.

Response table for tensile stress at break.

Level	AS	ASR	ASVC	HAR	HAS	HASV	0°	45°	90°
Mean S/N (dB)	7.16	8.18	13.17	13.62	9.72	18.64	10.30	12.23	12.71
Delta	–	–	–	–	–	11.48	–	–	2.41
Rank	6	5	3	2	4	1	3	2	1

In Tensile Strain at Break, the greatest effect is provided by orientation (Delta = 11.60) than core type (Delta = 7.75). ASR has the highest performance (16.99 dB) followed by ASVC (16.84 dB). The 0⁰ orientation has large strain superiority when compared to other orientations (Table 9).

Table 9.

Response table for tensile strain at break.

Level	AS	ASR	ASVC	HAR	HAS	HASV	0°	45°	90°
Mean S/N (dB)	13.66	16.99	16.84	12.62	13.81	9.24	19.96	13.27	8.36
Delta	–	7.75	–	–	–	–	11.60	–	–
Rank	4	1	2	5	3	6	1	2	3

Table 10 gives the average Signal-to-Noise (S/N) ratios calculated with the Larger-the-better criterion for all of the factors of the Taguchi experiment. The delta value, defined as the range of residual of the maximum and minimum average S/N ratio between the levels of the factor, is a measure of the relative importance of factors on the mechanical response. Raster angle has the most significant impact (Δ = 4.06, Rank 1), followed by core structure (Δ = 2.95, Rank 2), layer height (Δ = 2.29, Rank 3) and print speed (Δ = 2.02, Rank 4). Among the six core structures, S/N values vary between 56.50 dB (HAS) and 59.44 dB (HASV), which proves that HASV is the best performing geometry. These results show that raster angle and core structure are the main factors controlling the tensile behavior of FDM printed PLA sandwich structures and should therefore receive primary focus during the optimization of the process.

Table 10.

Response tables for S/N ratios with delta and rank.

Factor	Level 1	Level 2	Level 3	Level 4	Level 5	Level 6	Delta	Rank
Core Structure	57.52	58.82	59.17	57.61	56.49	59.44	2.95	2
Raster Angle	60.61	57.37	56.55				4.06	1
Layer Height	57.01	58.21	59.3				2.29	3
Print Speed	58.51	57.02	59.04				2.02	4

Key findings from the analysis

The current study shows that, in terms of Maximum Load, raster angle (orientation) and core structure are the variables with the highest influence (Delta = 4.06 and 2.95 respectively). The highest performance is obtained with 0⁰ orientation with the core of HASV considered. In case of UTS, the most significant variable is orientation (Delta = 3.84), whereas HASV obtained the highest values. In the case of Young’s modulus core architecture plays a slightly higher role than orientation (Core Delta = 3.11 vs. Raster Angle Delta = 3.03) with ASVC showing the largest S/N ratio (57.80 dB) followed closely by HASV with 57.77 dB confirming that indeed these two cores are the stiffest configurations. The Tensile stress at break shows that the core structure has the best impact (Delta = 11.48) and especially HASV performs the best. It is interesting to conclude that 90 degrees orientation presents superior stress results. Regarding Tensile Strain at Break, orientation appears the most conclusive variable (Delta = 11.60), and the ASR core fulfils with the performance at 0° orientation.

As a systematic investigation has shown (Fig. 13), the orientation, which is the angle of raster, is the major variable that will influence the maximum load, ultimate tensile stress (UTS), and tensile strain to break. On the contrary, the core structure type has the greatest influence on Young’s modulus and tensile stress at break. The best combination is usually obtained at 0⁰ orientation of HASV or ASVC cores which maximizes tensile strength and stiffness. With a complementary approach, the level of 0⁰ orientation of ASR and ASVC cores reaches maximum tensile strain at break. These results are able to provide fine-control parameters when choosing 3D-printing routines that facilitate optimization of mechanical properties of bio-inspired architectures.

Fig. 13.

Main effect plot for S/N ratio.

Table 11 shows the optimum parameters that were obtained with the Taguchi experiment, which is performed to optimize the average signal-to-noise (S/N) ratios of 3D-printed specimens and, therefore, increase the mechanical properties of biomimetic structures. The outcomes show that these are the best settings. The results inform the choice of process parameters to enhance all-round strength, stiffness and quality of 3D-printed parts and patterns. Observance of such ideals will give ready-made parts with mechanical properties that are not only strong but also reliable.

Table 11.

Summary table of optimal levels.

Factor	Optimal Level	Avg S/N (dB)
Core	HASV	59.44
Layer Height	0.20 mm	59.30
Print Speed	70 mm/s	59.04
Raster angle	00	60.61

Statistical analysis

ANOVA

ANOVA results and significance of factors

The assessment of the effect of the various core architectures and key FDM printing parameters on mechanical performance of 3D-printed PLA specimen is the main aim of this study. There are five dependent variables and four independent variables; maximum load, ultimate tensile strength (UTS), youngs modulus, tensile stress at the break, and tensile strain at a break is determined against four independent variables; core type, layer height, print speed, and raster angle.

Prior to performing the analysis of variance, the assumptions of normality and homogeneity of variance were checked. The Shapiro-Wilk test was performed to check the normal distribution of response variables, and Levene’s test was used to check the homoscedasticity. The results (Table 12) indicated that Young’s modulus followed a normal distribution (p > 0.05), whereas maximum load, UTS, tensile stress at break, and tensile strain at break showed slight deviations from normality (p < 0.05). However, Levene’s test confirmed that most of the response variables met the homogeneity of variance assumption. For Tensile Stress at break, the statistical test of Levene suggested that the variance of the data is unequal (p = 0.005), with increased variance in HASV specimens with 0⁰ raster angle. Given that group sizes are equal (n = 3 per group) and the model F-ratio is large, this isolated violation is not expected to impact on the validity of the conclusions of the ANOVA for this response variable. Since for balanced experimental designs, mainly for the comparison of means, the statistical analysis is believed to be valid because usually the classical statistical analysis is robust to deviations of the normality condition.

Table 12.

Normality and homogeneity tests for response variables.

Response Variable	Shapiro–Wilk Statistic	p-value	Normality	Levene Statistic	p-value	Variance
Maximum Load (N)	0.931	0.004	Deviation	0.459	0.635	Equal
UTS (MPa)	0.915	0.001	Deviation	0.255	0.776	Equal
Young’s Modulus (MPa)	0.980	0.506	Normal	1.440	0.246	Equal
Tensile Stress at break (MPa)	0.909	0.001	Deviation	5.814	0.005	Unequal
Tensile Strain at Break (%)	0.909	0.001	Deviation	1.105	0.339	Equal

JMP Pro software was used to perform one- way analysis of variance (ANOVA) with the purpose to assess the importance of each of the factors in the experiments. Statistical significance was tested at a confidence level of 95%, which corresponds to a significance level of α = 0.05. The p-values of all the response variables of the models were less than 0.0001 (Table 13), which would mean that the level of statistical significance is very high and one could reject the null hypothesis in each case. R² (adjusted) values were between 0.71 and 0.93, which show that the models explained the majority of the observed variance, with one exception (tensile stress at break, which is lower, R² = 0.71 yet is acceptable to interpret). The F-ratios ranged between 12.18 and 62.04, which depicts a significant effect of factors especially in tensile strength and strain (Table 16).

Table 13.

JMP profiler results: optimal process conditions and predicted mechanical performance with confidence intervals.

Property	R² Adj	Most Significant Factors	Model p-value	Model Validity
Maximum Load (N)	0.91	Core, Raster angle, Print speed	< 0.0001	Excellent
UTS (MPa)	0.92	Core, Raster angle, Print speed	< 0.0001	Excellent
Young’s Modulus (MPa)	0.90	Core, Raster angle, Print speed	< 0.0001	Excellent
Tensile Stress at Break (MPa)	0.71	Core, Print Speed	< 0.0001	Good
Tensile Strain at Break	0.93	Core, Raster angle, Print speed	< 0.0001	Excellent

Table 16.

Summary of ANOVA results for the effects of core structure and printing parameters on mechanical properties of 3D-printed PLA.

Parameters	Source	Degree of freedom	Sum of squares	Mean square	F	P-value
Maximum Load (N)	MODEL	9	2,350,174.1	261,130	51.54	< 0.0001
	ERROR	44	222,913.0	5,066
	TOTAL	53	2,573,087.1
Ultimate stress (MPa)	MODEL	9	389.43	43.27	58.75	< 0.0001
	ERROR	44	32.41	0.74
	TOTAL	53	421.83
Youngs Modulus (Mpa)	MODEL	9	868,982.25	96,553.6	44.90	< 0.0001
	ERROR	44	94,613.23	2,150.3
	TOTAL	53	963,595.48
Tensile stress (Mpa)	MODEL	9	275.47	30.61	12.18	< 0.0001
	ERROR	44	110.53	2.51
	TOTAL	53	385.99
Tensile strain (%)	MODEL	9	768.35	85.37	62.04	< 0.0001
	ERROR	44	60.55	1.38
	TOTAL	53	828.90

Core structure and raster angle were found to be the most important as the responses showed consequential F-ratios and effect sizes in all (p < 0.001). Print speed also proved to be statistically reliable in the majority of responses; however, it did not have a significant effect as core type and raster angle. Layer height was not significantly different (p ≈ 1.0), with close to zero coefficients- possibly because of cross-effects with other factors or failure to make enough independent variation in the test matrix. The raster angle with 0⁰ produced the highest constants in terms of stiffness and strength, and 90⁰ and 45⁰ produced negative results thereby confirming anisotropy of FDM printed structures.

The percentage contribution of each factor was calculated as (SS_factor /SS_total )×100 using Type III partial sums of squares obtained from the JMP Pro effect tests output, in order to quantify the relative influence of each process parameter on the mechanical response variables. Following ANOVA, Tukey’s Honest Significant Difference (HSD) post-hoc test (α = 0.05) testing was performed in JMP Pro of all statistically significant factors: Core structure, Raster angle and Print speed—to identify specific pairwise differences between factor levels. Layer height was not included for post-hoc analysis since it did not have a statistically significant effect for any of the five responses (p ≈ 1.0).

The Tukey HSD post-hoc test results found in Table 14 show statistically supported pairwise differences between factor levels for all five of the mechanical responses. For Core Structure, HASV was consistently in class A which turned out to be the ones with the highest values for Maximum Load, UTS, and Young’s modulus, while they ranked last for ductility (Tensile Strain for Break, class C), finding a statistically significant tradeoff between strength and ductility. ASVC and ASR came out to be the most ductile cores (group A for Tensile Strain) and this is consistent with the Taguchi S/N analysis. For Raster Angle, 0⁰ was significantly better than both 45⁰ and 90⁰ for all strength related responses (p < 0.001), however no significant difference was found between raster angle levels for Tensile Stress at Break (all group A, p > 0.05) corroborating the evidence that core geometry, rather than print direction, controls local stress distribution at fracture. For Print Speed, the higher speeds (65 and 70 mm/s) showed significantly higher strength and the 60 mm/s showed significantly higher ductility, so there is a trade-off between the speed of processing and the elongation at break.

Table 14.

Tukey HSD post-hoc pairwise comparison results (α = 0.05).

a—Core Structure
Core	Max Load (N)	UTS (MPa)	Young’s Modulus (MPa)	Tensile Stress at Break (MPa)	Tensile Strain at Break (%)
HASV	988.43 (A)	12.778 (A)	785.30 (A)	9.041 (A)	3.454 (C)
ASVC	920.39 (AB)	11.667 (AB)	781.52 (A)	4.653 (BC)	8.655 (A)
ASR	882.37 (B)	11.333 (B)	707.20 (B)	3.088 (C)	7.960 (A)
HAR	775.56 (C)	10.000 (C)	673.10 (B)	5.500 (B)	5.618 (B)
AS	766.15 (C)	9.889 (C)	662.17 (B)	2.700 (C)	5.692 (B)
HAS	694.93 (C)	9.000 (C)	562.88 (C)	3.473 (BC)	5.480 (B)

b—Raster Angle
Raster Angle	Max Load (N)	UTS (MPa)	Young’s Modulus (MPa)	Tensile Stress at Break (MPa)	Tensile Strain at Break (%)
0°	1087.0 (A)	14.019 (A)	846.53 (A)	4.741 (A)	10.632 (A)
45°	781.0 (B)	10.056 (B)	598.00 (C)	4.640 (A)	4.440 (B)
90°	645.9 (C)	8.259 (C)	641.56 (B)	4.825 (A)	3.358 (B)

c—Print Speed
Print Speed	Max Load (N)	UTS (MPa)	Young’s Modulus (MPa)	Tensile Stress at Break (MPa)	Tensile Strain at Break (%)
60 mm/s	773.48 (B)	9.907 (B)	670.34 (B)	4.224 (B)	7.182 (A)
65 mm/s	841.79 (A)	10.870 (A)	722.83 (A)	5.705 (A)	6.218 (A)
70 mm/s	898.63 (A)	11.556 (A)	692.91 (AB)	4.278 (AB)	5.030 (B)

Means followed by the same letter within each column are not significantly different (Tukey HSD, α = 0.05). LS Means reported. Post-hoc analysis conducted without Layer Height due to design singularity (p ≈ 1.0).

These inferences are supported by visual boxplot analyses (Table 15), which indicate that differences between the means of the various levels of factors are notable in the case of core type and raster angle. The HASV cores with 0⁰ raster orientation always produced the best maximum load, UTS and modulus. Layer height in its turn yielded overlapping distributions and insignificant effect. According to model diagnostics, there is a significant lack-of-fit in terms of some of the cases considered but the global pure error ratio is low and there is no clear graphical trend in terms of the residual plots. There is random distribution of the studentized residuals, which validates hypotheses of normality and homoscedasticity. These conditions justify the models in terms of main-effect analysis and contingencies.

Table 15.

Illustration of normal distributions of data and AnoVa.

As indicated in the current study, such optimization of core geometry and raster angle coupled with a calibrated print speed significantly affects the mechanical properties of poly lactic acid (PLA) FDM samples. The results show that in the case of the current design, the HASV core geometry with 0⁰ raster angle and a print velocity of ~ 65 mm/s will produce the best tensile properties. Layer height did not have a discernible effect under current conditions, but could be varied in future, as an independent parameter, to help understand interactions.

Table 16 presents the ANOVA summary for each mechanical property as obtained from JMP Pro software. ‘MODEL’ refers to the variability explained by the regression model including all factors, ‘ERROR’ indicates residual variance, and ‘TOTAL’ is their sum. F and P-values are as reported in the output. All models are highly significant (p < 0.0001).

A further quantification of the relative influence of each factor on the mechanical responses is provided in the percentage contribution analysis (Table 17). Raster Angle is found to be the leading contributor for Maximum Load (53.59%), UTS (55.58%), Young’s modulus (49.35%), and Tensile Strain at Break (50.18%) which confirms the leading role filament deposition direction plays in tensile performance of FDM printed auxetic structures. Core Structure accounts for the major contribution (30.01%) to Tensile Stress at break because of the role of geometric architecture in the control of the local stress distribution at the fracture. Print Speed shows an average but steady contribution on all responses (1.94–4.93%), while Layer height shows 0% contribution due to design singularity in L18 mixed orthogonal array. The low error contributions (7.31–28.64%) prove good model fitting and experimental reproducibility.

Table 17.

Percentage contribution of each factor to mechanical responses.

Factor	Max Load (N)	UTS (MPa)	Young’s Modulus (MPa)	Tensile Stress at Break (MPa)	Tensile Strain at Break (%)
Core Structure	3.69%	4.06%	5.15%	30.01%	17.69%
Layer Height	0.00%	0.00%	0.00%	0.00%	0.00%
Print Speed	4.12%	4.39%	1.94%	4.93%	3.79%
Raster Angle	53.59%	55.58%	49.35%	0.06%	50.18%
Error	8.66%	7.68%	9.82%	28.64%	7.31%

Percentage contributions (SS_factor/SS_total) x 100 using Type III partial SS from JMP Pro effect tests. Due to design singularity between Core Structure and Layer Height in the L18 mixed orthogonal array (LostDFs), the sum of contributions does not equal 100%. This is a known characteristic of mixed-level orthogonal arrays and does not have an influence on the validity of statistical conclusions.

Significant values are in bold.

Optimization using a least square fit method

JMP Pro software was used to identify the fit model tool to determine the optimum values. The initial stage of this process was defining the input parameter (type of core, the height of the layer, print speed, and raster angle) as an independent parameter and output parameters (maximum load, UTS, young’s modulus, tensile strain, tensile stress) as dependent parameters. The model was established as the Standard Least Squares, which means that the application did an ordinary least squares regression.

Figure 14 shows the scatter of dots plotting position in relation to actual and predicted values of each of the mechanical properties. The red lines are in form of data representing best-fit regression lines. The lines depict the anticipated values of the given actual values of the model, and the red-shaded parts around the regression lines are the 95% confidence intervals. The vertical differences between every data point and the regression line are considered the residuals between the observed and the predicted data. The scatter plots indicate that the relationship between the observations and respective regression lines is relatively close, and hence the goodness of fit for all the mechanical properties. The R-squared values show that about 91% variation in maximum load (R² =0.91), 92% in UTS (R² =0.92), 90% in Youngs modulus (R² =0.90), 71% in tensile stress at break (R² =0.71), 93% in tensile strain at break (R² =0.93) is explained by the model. These large R-squared measures underline the excellent correlation between the expected and the observed values.

Fig. 14.

Prediction profiler plot for various mechanical properties.

The very low P-values (< 0.0001) indicate that all regression models are statistically significant. The Root Mean Square Error (RMSE) values estimate the average prediction errors, with RMSE = 71.177 for maximum load, 0.852 for UTS, 46.371 for Young’s modulus, 1.585 for tensile stress, and 1.173 for tensile strain. Lower RMSE values indicate better model accuracy. As indicated by the P-values metric that is lower than 0.0001 in all regression models, the present study shows that this kind of the statistical analysis is appropriate. The values obtained by Root Mean Square Error (RMSE), which show average errors of the prediction, lead to RMSE = 71.177 as the maximum load, 0.852 UTS, 46.371 young’s modulus, 1.585 tensile stress, and 1.173 tensile strain. The smaller the RMSE the more accurate the model.

Figure 15 illustrates the prediction profiler plot that was essential in the identification of best combination of core type, layer height, print speed and raster angle that maximizes desirability with respect to predetermined mechanical property requirements. According to the graph, there is one parameter set that gives an optimal overall performance. The best combination of the optimized output shown in Table 15 shows that combination of HASV core structure, 0.2 mm layer height, 65 mm/s Print speed and 0⁰ raster angle provide the best balance reaching maximum loads of 1241.264 N, ultimate tensile strength (UTS) of 16.11 MPa, Young’s modulus of 963.936 MPa, tensile stress of 8.338 MPa and tensile strain of 6.816%. These findings also provide more comprehensive advice on future work aimed at ensuring utmost-performance of 3D-printed PLA components.

Fig. 15.

Prediction profiler plot.

The optimized results are illustrated in Table 18, which offers practical insights into potential future applications.

Table 18.

Optimized values obtained using ANOVA.

Setting	core	Layer Height (mm)	Print Speed (mm/s)	Raster Angle (°)	Maximum Load(N)	UTS(MPa)	Young’s Modulus (MPa)	Tensile Stress (MPa)	Tensile Strain (%)
Optimal	HASV	0.2	65	0	1241.2641	16.111111	963.9363	8.338	6.816%

Layer height (0.2 mm) is listed for practical fabrication reference only. ANOVA indicated that it was statistically indifference for total of five response (p = 1.0), no optimal level is formally designated.

Discussion on optimized settings

Design parameters

The HASV auxetic core was confirmed to be the most optimal core as it experienced the best internal support, load distribution, and energy absorption which led to the highest load carrying capacity, UTS and modulus values in comparison to all the tested geometries. Deposition of the filaments along the tensile loading axis at the 0⁰ raster angle allowed maximum stiffness and strength due to optimal load transfer and reduced stress concentration, which verified the anisotropic nature of FDM parts.

Process parameters

The empirical evidence showed moderate print speed (65 mm/s) provided the best trade between the quality of the deposition and manufacturing rate. Speeds outside this range have caused a negative impact on interlayer bonding and the tensile strength and print speeds lower than the limit created minimal enhancements in performance. Since layer height was found to be statistically insignificant (p = 1.0), no optimal level is formally designated. The value of 0.2 mm is noted for practical fabrication consistency only.

Anisotropy and multi-objective performance

This overwhelming performance advantage of the 0⁰ orientation compared to both 45⁰ and 90⁰ showed deep directionality in performance of printed parts. Optimized parameter set (HASV, 0⁰, 65 mm/s, 0.20 mm) reached an estimated ultimate load of ~ 1241 N, UTS of 16.1 MPa, and elastic modulus of approximately 964 MPa, tensile stress at break of 8.3 MPa and strain at break of 6.8%, a reasonably good compromise between toughness and strength. Cohesion with Taguchi methodology and a desirability of 0.722 shows that this is a robust combination to improve the mechanical performance without losing manufacturability and as such a combination is desirable in high load functional requirements.

The results demonstrate a clear directional dependence in the mechanical performance of the printed specimens. The 0° raster orientation produced higher strength and stiffness compared with the 45° and 90° orientations, indicating the influence of filament alignment relative to the loading direction. The optimized parameter combination (HASV core structure, 0° raster angle, 65 mm/s print speed, and 0.20 mm layer height) yielded a predicted maximum load of approximately 1241 N, UTS of 16.1 MPa, and Young’s modulus of about 964 MPa, with tensile stress at break of 8.3 MPa and strain at break of 6.8%. These results indicate a balanced mechanical response between strength and ductility. The Taguchi multi-response optimization produced a desirability value of 0.722, indicating that this parameter combination improves tensile performance while maintaining practical manufacturability for load-bearing PLA components.

The results show an obvious direction dependence in mechanical performance of the printed specimens. The 0° raster orientation resulted in higher strength and stiffness than the 45° and 90° orientations with the influence of the alignment of the filaments to the loading direction.The best combination of parameters (HASV core structure, 0 degrees raster angle, 65 mm/s print speed, and 0.20 mm layer height) obtained the following results: The predicted values of maximum load, UTS value and Young’s modulus value were about 1241 N, 16.1 MPa and 964 MPa, respectively; the tensile stress at break value and the strain at break value were 8.3 MPa and 6.8%, respectively.These results indicate a balanced mechanical response between the strength and the ductility. The Taguchi multi response optimization resulted in a desirability value of 0.722, which means that this combination of parameters enhances the tensile performance while ensuring practical manufacturability in load bearing PLA components.

Relation to Taguchi Methodology and Research Significance

These optimized values align with the principles of the Taguchi design of experiments, wherein the highest signal-to-noise (S/N) ratios are used to identify robust and influential factors. The pronounced effects of the HASV core structure and 0° raster angle underscore the critical role of structural and directional parameters in additive manufacturing. The overall desirability score of 0.722 indicates a strong effectiveness and balance of the optimized parameter combination across multiple mechanical properties. This parameter combination optimizes strength while maintaining adequate ductility, making it suitable for structural applications requiring high load-bearing capacity. Presenting these findings demonstrates how a combination of well-planned experimental design and statistical optimization can effectively guide engineers toward process conditions that maximize functional performance while ensuring feasible manufacturing.

The mechanical performance of 3D-printed PLA specimens varies significantly across different core structures and raster angles, as illustrated in Fig. 16. The HASV core structure at 0° raster angle consistently demonstrates superior mechanical properties, exhibiting the highest maximum load (approximately 1100 N), ultimate tensile strength (approximately 15 MPa), and Young’s modulus (approximately 950 MPa). This finding aligns with our Taguchi analysis, which identified HASV core and 0° raster angle as optimal parameters. In contrast to some previous studies³ that found 90° raster angles optimal for certain PLA applications, our results show that the 0° raster angle consistently outperforms 45° and 90° orientations across most core structures, especially for load-bearing capacity and tensile strength. This discrepancy may be attributed to the unique infill patterns of our core structures and the specific grade of PLA used. The effect of raster angle on mechanical properties can be explained by load alignment with the printed filaments; when the tensile load direction coincides with the filament orientation (0°), the specimen exhibits higher strength and stiffness, as noted by Hossain et al.⁴ and Masood et al.⁵. However, the tensile strain at break shows a different pattern, with certain configurations like AS at 0° demonstrating higher ductility despite not having the highest strength. This inverse relationship between strength and ductility is consistent with findings from Chacon et al.⁵, suggesting that optimizing for one mechanical property may require compromises in others. These empirical findings validate both our ANOVA results identifying core structure and raster angle as the most significant factors (p < 0.0001) and provide the foundation for the subsequent ANN model development.

Fig. 16.

Mechanical properties of 3D-printed PLA specimens with different core structures and raster angles. (a) Maximum Load (N); (b) Ultimate Tensile Strength (MPa); (c) Young’s Modulus (MPa); (d) Tensile stress at Break (MPa); (e) Tensile strain at Break (%).

ANN prediction

An ANN model was developed to predict the mechanical properties of 3D-printed PLA specimens depending on the critical process and structural parameters. The model was trained in the Neural Fitting Tool of MATLAB (nftool) and trained using Bayesian regularization (BR) as the training algorithm, which was chosen over the simpler Levenberg-Marquardt method due to the problem of overfitting concern inherent in small experiment datasets. The ANN used a feed forward back prop architecture with 4 inputs (core type, layer height, print speed and raster angle), one hidden layer with 10 neurons and 5 outputs (maximum load, UTS, Youngs modulus, tensile stress at break and tensile strain at break) as given in Sect.  2.7 (Figs. 8 and 10). The regularized objective function (Eqs. 1–2) implemented in Bayesian Regularization as described in Sect.  2.7 uses the entire dataset of 54 specimens to learn the model by preferential loss of model complexity, with the regularized objective function eliminating 105 nominal parameters in favor of only 75.46 effective parameters and eliminating the need to have a separate validation set. Regression plot (Fig. 17) indicates correlation coefficients of R = 0.97534 (training), R = 0.97828 (test) and R = 0.97583 (overall) indicating that there is a strong linear relationship between predicted and experimental value in all five mechanical outputs. The regression equation (Output ≈ 0.94 × Target − 0.013) shows that the slope of the regression line is close to unity, and the intercept is close to zero, which suggests that systematic bias in the model predictions is low.

Fig. 17.

Regression plot.

The performance plot (Fig. 18) shows that the network converged at epoch 76 to the best normalized MSE = 0.013018 on data on the interval [-1, 1]. The train and test curves are close to each other throughout 229 epochs, proving stable training with no divergence. The training state plot (Fig. 19a) validates the stability of convergence based on the smooth decrease of gradient to 0.0022932, stable mu oscillation and effective parameter count, and this is maintained to 75.46 for 229 epochs. Validation checks were continuously at zero during training, as expected under Bayesian Regularization as this algorithm is based on maximizing evidence rather than early stopping as a convergence criterion.

Fig. 18.

Performance.

The error histogram (Fig. 19zab) shows that there is a symmetric, near-zero centralized distribution with prediction error of − 6% to + 5% on all the five mechanical properties with most of the prediction error being within ± 2%, which confirms unbiased and normally distributed predictions. Figure 19c presents the signed prediction error distributions for each mechanical property individually. Errors around zero are observed in all five properties including Maximum Load (mean = − 0.25%), UTS (mean = − 0.28%), Young’s modulus (mean = 0.12%), Tensile Stress at break (mean = − 0.95%), and Tensile Strain at Break (mean = − 0.41%) and indicate the absence of systematic over or under-prediction bias in all outputs. The corresponding mean absolute errors were 1.58% (Maximum Load), 1.33% (UTS), 1.0% (Young’s modulus), 2.44% (Tensile Stress at break), and 3.51% (Tensile Strain at Break). To verify the generalization capability of the model obtained independent of the cross-validation, a 5-fold cross-validation on the entire dataset (54 specimens) was conducted. The dataset was partitioned into 5 equal subsets, with each subset serving once as the test set while the remaining four subsets were used for training. The R values were obtained as 0.9640, 0.9646, 0.9637, 0.9613 and 0.9538 over the five folds giving an average result of R = 0.9615 with standard deviation of 0.004 (Table 19). The high and low-reliable R values throughout the folds affirm that the model is a reliable prediction of non-observed data and eventually overfitting is ruled out.

Table 19.

5-Fold cross-validation.

Fold	R Value
Fold 1	0.964
Fold 2	0.9646
Fold 3	0.9637
Fold 4	0.9613
Fold 5	0.9538
Mean ± SD	0.9615 ± 0.004

Raster angle and core structure were identified as the dominant parameters affecting ANN predictions, while layer height showed minimal influence within the investigated range — consistent with the mechanics of FDM structures where filament orientation controls load transfer and core architecture governs stress distribution. This confirms that the ANN predictions reflect physically meaningful input–output relationships rather than black-box correlations.

Fig. 20.

Comparison of actual, predicted, and error values for key mechanical properties across experiments.

Figure 20 shows a detailed comparison of actual and predicted values and percentage errors of all 18 experimental conditions for five mechanical properties. All predictions were given a maximum of error of ± 6.4%, and the total mean absolute blame for all properties and runs was 1.97%. These results confirm the robustness and reliability of ANN model under different combinations of the process parameters. The results show that ANN with Bayesian regularization can be effectively used as a decision support factor for optimization of FDM process parameters for bio-inspired PLA structures—thus eliminating the need for time-consuming physical experiments. This approach can help to reduce wastage of materials, shorten design cycles and accelerate the development of lightweight and high-performance biomimetic structures.

Fig. 19.

(a) Training state, and (b) error histogram for all properties. (c) Distribution of ANN Prediction Errors for All Mechanical Properties.

Discussion

Interpretation of results in context of research questions

The experimental results showed a large variation of the tensile mechanical properties on different core structures and raster orientations. Specimens printed with a 0° raster angle were able to carry out more loads as the direction of filaments deposition was parallel to the direction of the applied tensile force, and therefore, maximized resistance was achieved. Conversely, 45° and 90° orientations demonstrated lower UTS and Young’s modulus attributable mostly to their use of the interlayer bonding - an inherent weakness of FDM⁴⁴. Core structures like AS and ASR exhibited similar performance indicators (maximum load, UTS, tensile strain at break) in line with previous experiments on 3D printed PLA, although values are still lower than injection moulded ones. These findings all together elucidate on the mutual interrelation between design variables and mechanical performance, providing practical guidance for PLA component design using the additive manufacturing constraints.

The aim of the study was to address major questions on the mechanical character of bio-inspired 3D-printed PLA samples and optimization of the printing settings. The results clearly indicate that bio-inspired core structure and raster angle exert the strongest influence on tensile mechanical properties—including maximum load, ultimate tensile strength (UTS), young’s modulus, tensile stress, and strain at break—of the tested specimens. In particular, samples printed using the HASV core structure and a 0⁰ raster angles always showed better strength and stiffness. The current research demonstrates that the print speed has a moderate, but significant effect on mechanical properties, which means that the deposition rate remains an essential thing to control. At the same time, the height of layer demonstrated no independent influence, possibly due to confounding factors and the narrow scope of independent variation.

The Taguchi technique with the combination of ANOVA were used to optimize the setting and identify the most dominant factors in the FDM processing. The results validate that Taguchi design can be used to accurately determine the optimal settings of a process for the effective screening of the critical parameter levels in a more complicated, multi-parametric screening study. Further, non-linear interactions among the input parameters could be understood from output of ANN model with high predictive accuracy which has reduced the number of physical experiments for mechanical properties evaluation.

Comparison with previous literature

Mechanical optimization with bio-inspired auxetic-core structures in this present research does contribute considerably to the existing state of knowledge, as it is being done concurrently with validation of traditional results in fused deposition modelling (FDM). Past studies (Table 20) have concluded that raster angle is the main factor that determines the tensile strength (Rajpurohit & Dave, (2018); Lokesh et al., (2022)) and this can also be seen in the results presented here as the reported results on HASV cores oriented at 0⁰ (UTS 18.3 MPa; maximum load 1,426 N)^42,43. Unlike those previous investigations, the current data show that layer height has no statistically significant effect, presumably because the auxetic geometries involve so many constraining elements that sensitivity to nominal thickness change is reduced.

Table 20.

Literature comparison with present study.

References	Key Finding (Cited Paper)	Results Reported in Cited Study	Comparison with Present Study
Rajpurohit & Dave (2018)42	0° raster angle optimal; lower layer height beneficial	High value of UTS obtained at 0° raster	Confirms 0° optimal (HASV 0°: 18.3 MPa UTS)
Caran et al. (2024)31	Alternative core structures enhance compressive strength	Compressive strength 9.867 MPa, 32–54% higher than conventional cores	Supports optimized internal geometries; extends to bio-inspired auxetic cores for tensile properties
Lokesh et al. (2022)43	Raster angle most influential (64.96%) on tensile strength via Taguchi	Optimal at 80% infill, 40 mm/s speed	Confirms raster angle dominance (Delta = 4.06, rank 1); contradicts layer height significance; our insignificant finding, likely due to different core complexities
Subramonian et al. (2023)20	ANN achieved high predictive accuracy for FDM PLA properties	ANN: R² = 0.985–0.988; <5% prediction error	Our ANN: R² = 0.975, < 5% error, trained on bio-inspired core datasets
Kumar & Kumar (2025)45	Taguchi optimization confirms 0° raster angle and 30 mm/s speed yield highest tensile strength	Tensile strength peaked at 0° raster angle; speed and layer height also significant	Consistent with present study; confirms optimal raster angle and supports parameter sensitivity
Ramírez-Prieto et al. (2025)46	0°/0° raster angle delivers highest strength; confirms anisotropic behavior	Tensile and flexural strength highest at 0°/0°; mechanical response varies with angle	Matches present findings; reinforces directional dependence of strength
Abdolvahed et al. (2024)47	ANN model achieves high accuracy (R² > 0.98); validates AI-based prediction approach	ANN predicted tensile strength with minimal error; confirms model reliability	Strong alignment; supports use of ANN in mechanical property prediction.
Tan et al. (2023)48	Infill density/raster angle effect	UTS up to 28.9 MPa (100% infill, 0° raster); lowest (17.3 MPa) at 30% infill, 90° raster)	Confirms infill and raster orientation strongly affect strength.

The transition to bio-inspired core architectures represents a significant advancement in the additive manufacturing sector. The same was observed when Caran et al. (2024) investigated new core patterns (32–54% increase in compressive strength)³¹. The current paper on auxetic designs shows that tensile performance can also be enhanced by negative Poisson ratio (NPR) and energy-absorbing structure based on natural designs. Models that allowed computing the traditional cores represented them with a neural network (Subramonian et al., (2023))²⁰; the predictive accuracy of those approaches were high (R² ≈ 0.988, error < 5%) on taditional cores; an ANN trained on bio-inspired datasets was able to achieve similar levels of accuracy and predict optimal parameters (0⁰ raster angle, 70 mm/s print speed). Proposed bio-inspired cores have been experimentally proved, and HASV core architecture showed versatile characteristics that comprised great tensile strength and energy absorption.

Recent studies have confirmed and expanded knowledge regarding the impact of parameters in FDM. According to Kumar & Kumar (2025), based on Taguchi optimization studies, the maximum tensile strength is attained with a 0° raster angle and 30 mm/s speed, which supports our findings⁴⁵. Ramírez-Prieto et al. (2025) showed the most pronounced anisotropy with the highest tensile and flexural strength at 0°/0° raster orientation, supporting the directional dependency described here⁴⁶. Abdolvahed et al. (2024) supported the AI models with prediction results from ANN over 0.98 R², and error values AI models with ANN prediction results over 0.98 R² and minimal error, confirming the approach used⁴⁷. According to Tan et al. (2023), infill density and raster angle are of primary importance, with a maximum UTS of 28.9 MPa attained at full infill and 0° raster, which aligns with the confirmed strong raster orientation effect in this current research⁴⁸.

FDM has long been recognized for enabling complex shape fabrication, though it traditionally shows lower mechanical properties relative to conventional manufacturing. This study shows that auxetic bio-inspired HASV architectures can perform comparably or better than standard benchmarks, marking a significant leap in FDM innovation. Table 15 offers a comparative summary validating these findings against key prior works, underlining both continuity and advancement in the field.

Explanation of factor effects and interactions

Core geometry has a significant effect on the performance of the structure by influencing the cellular distribution of the lines of thrust in order to control the load paths and the failures. Thick-walled and interlocking core unit are bio-inspired and are more useful where, stress violation concentrations are reduced and the maximum loads and high elastic moduli are permitted. Raster angle can be used to alter the inherent anisotropy of FDM parts setting the direction of fibers with respect to the principal loading direction: the 0-degree raster angle positions the path of the filament in line with tensile loading, maximising the load being carried.

Print speed is such an important variable to identify the quality of filament bonding and residual stress. The time taken to print seems to moderate the adhesion, therefore leading to slower printing in general improving it, and faster printing decreasing mechanical properties, so there exists such range of rates, where moderate effect takes place, where the quality-efficiency ratio can be optimized. In the current study, layer height did not prove independent significance and the explaining reasons are probably the confounding effect with core structure and the inadequacy of parameter levels spacing in the used experimental matrix. This interaction points to a need to utilize experimental designs which hold constant individual factor effects in a better way.

Implications for design and manufacturing of PLA core structures

The results provided in the present study lead to a number of practical implications or conclusions on the part of the practitioners, the first one being those designers and producer willing to create more mechanically sound but at the same time, lightweight PLA components ought to consider bio-inspired and their core architectures, namely HASV, along with the raster orientation of 0⁰. Second, when the goal of maximizing print speed, about 70 mm/s, is attained, it is providing a reasonable trade-off between the mechanical performance and the build-time performance. The subtle understanding of the interactions of core structure and raster angle would allow a more direct, data-oriented specification of process parameters, thus disavowing the trial-and-error methodology and raising the part performance predictability. This is critical for high-performance applications in aerospace, biomedical devices, and custom structural components.

Limitations of the study

While the study gives comprehensive insights, limitations include the effect of possible confounding effects that prevented independent evaluation of the role of layer height that might mask more subtle influence of this parameter. The scope was limited to PLA material and certain printer settings, without being able to generalize to the other materials or hardware. The experimental investigation in this study was done using JAMG HE High-Speed PLA filament and Pratham 3.0 FDM printer with controlled process conditions. While such an approach guarantees consistency of the experiments, the absolute values of mechanical responses may differ when different PLA formulations, printer architectures or extrusion systems are used. The differences in polymer composition, melt viscosity, crystallinity, and the additives added can affect the bond between the layers and the mechanical properties. Similarly, printer specific characteristics “like extruder configuration, temperature control and motion accuracy” may affect layer deposition quality. Nevertheless, the major trends identified — especially the strong dependence of tensile behavior on raster orientation and core geometry — are governed by fundamental FDM anisotropy and structuring mechanics of bio-inspired cellular architectures, and expected to be broadly applicable to similar FDM based PLA structures. Furthermore, the combined Taguchi-ANOVA-ANN methodology developed and presented here could be readily adapted and used for other materials-process combinations in additive manufacturing. Interactions between factors other than main effects were not modelled completely because of constraints on the design and the long-term mechanical behavior (e.g., fatigue, environmental aging) was not taken into account. Future work should remedy these gaps by making use of a full factorial or RSM design — especially to quantify the interaction of the raster angle and core geometry, which the current L18 design was not arranged to measure — as well as to expand the evaluation of material types and include durability evaluations.

Conclusion

Summary of key findings

This research investigated the mechanical behaviour of 3D-printed PLA specimens with six bio-inspired core structures under varying printing parameters, employing a combined Taguchi-ANOVA and ANN modelling approach. Core structure and raster angle emerged as the most influential factors governing tensile mechanical properties, with the HASV core and 0° raster angle providing optimal strength and stiffness. Print speed was a significant secondary factor, whereas layer height was not significant under the current experimental design. The adoption of Bayesian Regularization comprising of 10 hidden neurons by using 5-fold cross validation (mean R of ANN = 0.9615) proved the ANN ability to generalize the mechanical properties prediction without overfitting, thus it constituted a reliable tool for virtual optimization FDM process parameters.

Practical recommendations for 3D printing parameters and core design

For enhanced mechanical performance in FDM-printed PLA components, it is recommended to employ bio-inspired core structures like HASV, align raster angle at 0° with the primary load direction, and maintain print speeds near 70 mm/s. These settings balance mechanical strength, stiffness, ductility, and production efficiency. Layer height effects require further study before firm recommendations can be made.

Suggestions for future research

This study demonstrates the effectiveness of Taguchi experimental designs complemented with ANOVA and ANN to uncover and optimize the principal process parameters affecting the mechanical performance of bio-inspired 3D printed PLA structures. Although the Taguchi method is useful in screening the major factor effects and enabling robust statistical optimization, it precisely lacks the ability to disentangle the interaction effects of the parameters, as was the case of the layer height in this study. Hence, it is recommended that future studies utilize factorial experimental designs (full or fractional) to determine the interactions and main effects more systematically. This method will better describe the inter-dependencies of the parameters and better explain the influence of layer height and other less meaningful features. Evaluating additional polymers and printer models, alongside a detailed assessment of the impact of climatic variations on the performance degradation, would enrich the external validity and enhance the practicality of the outcome. Finally, using more sophisticated, multi-objective optimization techniques, coupled with machine learning, other than the ANN, would strengthen the findings of this research, as it would greatly enhance predictive precision, facilitate real-time process control, and fast track the growth of high-performance additive manufacturing processes.

Abbreviations

AM

Additive manufacturing

FDM

Fused deposition modeling

PLA

Polylactic acid

CAD

Computer aided design

ANOVA

Analysis of variance

ANN

Artificial neural network

HC

Honeycomb cell

HCR

Honeycomb cell with rounded corners

HCVC

Honeycomb cell with varying cross section

HCL

Honeycomb cell with lamellar curve

HCRL

Honeycomb cell with rounded corners and lamellar curve

HCLVC

Honeycomb-lamellar curve with varying cross Section

AS

Auxetic structure

ASR

Auxetic structure with rounded edge

ASVC

Auxetic structure with varying cross section

HAS

Hexagonal auxetic structure

HAR

Hexagonal auxetic structure with rounded edge

HASV

Hexagonal auxetic structure with varying cross section

STL

Standard Tessellation Language

SEM

Scanning electron microscopy

ASTM

American Society for Testing and Materials

SD

Standard deviation

Author contributions

Sirajudeen Inayathullah 1 - Conceptualization, Formal analysis, Investigation, Methodology, Resources, Writing – original draft.Raviteja buddala 2 - Supervision, Validation, Writing – review & editing.

Funding

Open access funding provided by Vellore Institute of Technology.

Data availability

The datasets generated and/or analysed during the current study are not publicly available due to institutional data-sharing restrictions, but are available from the co-author, Sirajudeen Inayathullah, upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.