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Abstract

This work focuses on optimizing the mechanical and electromechanical properties of a 3D-printed strain-sensing prosthetic socket fabricated using a conductive PETG-based composite (P15LT35 G) via Fused Deposition Modelling (FDM). A full factorial design (3³) was implemented to study the influence of nozzle diameter (0.4, 0.5, 0.6 mm), infill pattern (grid, lines, gyroid), and infill density (30%, 50%, 70%) on performance characteristics. The socket was evaluated through tensile, flexural, impact, and compression testing, with the best configuration (0.4 mm nozzle, grid pattern, 70% infill) yielding a peak compressive strength of 25.62 MPa and a flexural strength of 31.72 MPa. Electrical characterization revealed that the optimized sensor exhibited a gauge factor of 1.52 with a nonlinearity coefficient of 4.01 under cyclic loading, indicating stable piezoresistive behavior. The low sensitivity, denoting controlled resistance changes under uniform loading, enhances signal reliability for limb-socket interface monitoring. ANOVA and Response Surface Methodology (RSM) were used to develop predictive models with high significance (p < .05) and adjusted R² values exceeding 95%. The final prosthetic socket design includes embedded sensor paths and ventilation zones, validated through load simulations and experimental tests. The study demonstrates a robust approach for integrating sensing capability within structural components, offering a scalable solution for smart prosthetic systems.

Keywords

3D printing PETG strain sensor FDM ANOVA

Introduction

Prosthetic limbs play a crucial role in restoring mobility and improving the quality of life for individuals who have undergone amputation due to injury or disease. Among various components of a prosthetic limb, the prosthetic socket is particularly important as it provides a secure interface between the residual limb and the prosthetic structure. Ensuring proper fit and functionality of the socket is critical for comfort, stability, and long-term usability.^1,2 However, traditional fabrication methods, which include impression taking, positive mold creation and fabrication around the mold,³ often result in inconsistencies due to manual casting techniques, leading to irregular tension distribution and poor load-bearing characteristics. These inconsistencies affect the overall structural integrity and comfort of the prosthetic socket, making it difficult to achieve a precise fit for every individual.^4–8

To overcome these challenges, 3D printing technologies, particularly Fused Filament Fabrication (FFF),⁹ have emerged as a promising solution for manufacturing customized prosthetic sockets.^10–12 FFF enables precise control over processing parameters, allowing the production of prosthetic components with optimized mechanical properties and embedded functionalities, such as strain sensing.^13,14 While various thermoplastic polymers, such as PLA, ABS, and PETG, have been explored for 3D-printed prosthetics, there is limited research on integrating conductive composite materials into prosthetic sockets for real-time strain sensing applications.^11,15 Singh et al.¹⁶ found that PLA composites achieve maximum mechanical strength when printed with 100% infill density, with further improvements obtained through Taguchi methodology (TM)-based optimization. Osman Ulkir and Gazi Akgun¹⁷ investigated the mechanical performance of FDM-printed ABS, identifying infill density, layer height, and printing speed as key factors influencing compressive strength. Their optimized process achieved a peak compressive strength of 55.76 MPa. Ning et al.¹⁸ conducted a study on the mechanical properties of 3D-printed samples incorporating varying carbon fiber concentrations within an ABS polymer matrix. Their findings revealed that carbon fiber reinforcement led to a 22% increase in tensile strength, a 31.6% improvement in Young’s modulus, and an 11.8% enhancement in bending strength. Additionally, Dhruv Maheshkumar et al.¹⁹ investigated the impact of infill pattern (IFP) on tensile strength, surface roughness, and processing time, highlighting the significance of infill geometry in determining the overall mechanical performance and print efficiency of FFF-fabricated components.

Over time, numerous studies have focused on optimizing printing parameters and design processes to enhance the strength and performance of 3D-printed prosthetics.^20–24 However, one of the major challenges in prosthetic socket design remains the accurate identification of pressure points and interfacial stresses between the residual limb and the socket.¹² Uneven load distribution can result in discomfort, instability, and pressure sores, ultimately compromising the effectiveness of the prosthesis. Despite advancements in 3D-printed prosthetic sockets, most designs lack an integrated system for real-time stress monitoring, making it difficult to achieve a precise and customized fit for individual users.^25–30

For an instance, recent research by Sachin et al.³¹ explored the use of PETG for fabricating 3D-printed orthoses such as long arm casts, emphasizing improved comfort, ventilation, and mechanical strength. Their study showed that increasing infill density from 40% to 60% enhanced tensile strength from 30.93 MPa to 33.9 MPa and flexural strength from 44.3 MPa to 55.22 MPa, demonstrating PETG’s suitability for sustained load-bearing applications. Moreover, their finite element analysis favored hexagonal pores for higher safety factors under physiological loads. This underlines PETG’s growing acceptance in orthotic design. Other recent researches^32–34 also explore the increasing application of PETG in the form of composites, highlighting its biocompatible properties.

The current study aims to fabricate a universal prosthetic socket embedded with a strain sensor capable of identifying stress distribution and pressure points in real time. By incorporating a conductive PETG-based composite material, the prosthetic socket can sense strain at critical load-bearing regions, enabling refined and customized prosthetic designs for better load management, enhanced comfort, and improved long-term performance for amputees. Various PETG-based conductive composites were developed and analyzed, with P15LT35 G (15% lithium titanate oxide + 35% graphene nanoplatelets) selected based on its superior electrical conductivity. The mechanical properties of P15LT35 G were evaluated through compressive strength (CS), impact strength (IS), and flexural strength (FS) tests to ensure its durability in prosthetic applications. Additionally, ANOVA was employed to optimize the fabrication process by analyzing key printing parameters, including Nozzle Hole Diameter (NHD) (0.15 mm, 0.25 mm, 0.4 mm) and Infill Pattern (IFP) (Grid, Tri-Hexagon, Honeycomb). Finally, the optimized P15LT35 G composite was integrated into a 3D-printed prosthetic socket, embedding the strain sensor for real-time stress monitoring and improved pressure distribution, ensuring a more functional and user-specific prosthetic solution.

While prior studies have explored PETG in the design of orthoses and orthopedic braces, this study is the first to investigate a functional strain-sensing application using P15LT35 G, a conductive PETG-based composite, integrated directly into 3D-printed prosthetic sockets. P15LT35 G offers a unique combination of structural support and piezoresistive sensitivity, enabling embedded sensing without additional post-processing or external wiring. To the best of the authors’ knowledge, this is the first reported use of this specific conductive PETG formulation for embedded strain sensing in a prosthetic application, addressing both mechanical performance and functional integration simultaneously. Therefore, the aim of this study is to optimize the process parameters for 3D printing P15LT35G-based composites to achieve strain-sensing capabilities suitable for prosthetic sockets, while ensuring mechanical robustness, user comfort, and sensor reliability.

Materials and Methods

Materials

PETG pellets (MFI: 14 g/10 min, Tm: 170°C, purity >95%) were sourced from Rameshwar Manufacturing Solutions. Dichloromethane (DCM), lithium manganese oxide (LMO), and lithium titanate oxide (LTO) were obtained from Sigma Aldrich. Conductive additives—carbon fibers (CF: 3–5 µm dia., 160–220 µm length, >95% purity), graphene nanoplatelets (GNP: 25 µm size, 7–8 nm thickness, >98% purity), and multi-walled carbon nanotubes (MWCNT: 8–14 nm dia., 2–3 µm length, >98% purity)—were procured from Cubics 3D. LMO and LTO spinels had particle sizes <400 nm and <180 nm, respectively, with purities >95%.

After conducting tests for electrical conductivity on all the samples, P15LT35 G composite stands suitable for the application. The P15LT35 G composite exhibits a glass transition temperature (Tg) of approximately 80°C, a melting point of 230 – 260°C, and a melt flow index (MFI) of 18–22 g/10 min (at 250°C, 2.16 kg), making it suitable for FFF-based 3D printing. Thermogravimetric analysis (TGA) confirmed a thermal degradation onset at ∼330°C, indicating thermal stability during high-temperature processing. These properties support its application in thermomechanical demanding environments such as prosthetic sockets.

Followed methodology

Various conductive composites of PETG were first procured to additively fabricate electrical conductivity test specimens. The electrical conductivity test was performed on these PETG composites’ samples. This was done to obtain the optimal composite to be used as the strain sensing element in the PETG prosthetic socket. P15LT35 G was found to be the suitable material after testing the electrical conductivity of various composites as given in Table 1. This material was thus fabricated to produce the mechanical testing specimens. The mechanical testing was thus performed to tabulate CS, IS and FS. These experiments were performed by variating NHD and IFP. NHD has three values of 0.15 mm, 0.25 mm and 0.4 mm. Also, the IFP used for the testing were TH, HC and GD. Further, the statistical analysis was done to find the optimized conditions. Ultimately, the prosthetic socket of PETG is embedded with the P15LT35 G as the strain sensing material according to the statistically finalized process parameters. The overall working methodology followed in this study is illustrated in Figure 1.

Table 1.

PETG composites used for electrical conductivity testing and their codes.

S.No.	Material	Material code
01	Pure PETG	PETG
02	5% CF with PETG	P5C
03	10% CF with PETG	P10 C
04	15% CF with PETG	P15 C
05	20% CF with PETG	P20 C
06	5% GNP with PETG	P5G
07	10% GNP with PETG	P10 G
08	15% GNP with PETG	P15 G
09	20% GNP with PETG	P20 G
10	5% MWCNT with PETG	P5M
11	10% MWCNT with PETG	P10 M
12	15% MWCNT with PETG	P15 M
13	20% MWCNT with PETG	P20 M
14	4% LMO spinel and 16% MWCNT with PETG	P4LM16 M
15	6% LTO spinel and 24% GNP with PETG	P6LT24 G
16	12% LMO spinel and 23% MWCNT with PETG	P12LM23 M
17	15% LTO spinel and 35% GNP with PETG	P15LT35 G

Figure 1.

Work methodology.

Fabrication of filament materials

PETG pellets were pre-dried at 90°C for 3 h. Pure PETG filaments were directly extruded post-drying. For composite filaments, PETG was dissolved in DCM (0.1 g/mL) and stirred for 14 h, followed by addition of CF, GNP, MWCNT, LMO, and LTO. The mixture was cast on a Teflon sheet and left overnight for solvent evaporation. Dried composites were pelletized, re-dried at 80°C, and extruded at 175 °C–180 °C into 2.80 mm filaments. Finished filaments were stored in airtight bags with desiccants. A total of 17 filament variants were prepared, including pure PETG and PETG reinforced with various filler combinations (refer Table 1).

Electrical conductivity

The electrical conductivity of the developed PETG composites was evaluated to assess their potential for electrochemical electrode applications (Figure 2). Pure PETG showed negligible conductivity (4.61 × 10⁻¹¹ S/cm, E1), due to its non-conductive polymer matrix composed of ester linkages, which lack free electron pathways.

Figure 2.

Electrical conductivity variation.

Incorporating conductive fillers significantly improved conductivity by forming percolating conductive networks within the polymer. With 5% CF, conductivity increased to 0.06 S/cm (E2) and further rose to 0.24 S/cm (E5) at 20% CF, attributed to better alignment and interconnection of CFs enhancing electron flow. Lower CF content, however, results in isolated conductive zones, limiting conductivity.

PETG with 20% GNP (P20 G) reached 0.36 S/cm (E9), outperforming 20% MWCNT (P20 M) at 0.23 S/cm (E13). GNP’s high surface area and aspect ratio contribute to superior charge mobility, while MWCNTs often suffer from agglomeration, introducing interfacial resistance.

A combination of 4% LMO +16% MWCNT (P4LM16 M) improved conductivity to 0.39 S/cm (E14), showing enhanced charge transport due to LMO-facilitated ionic conduction alongside MWCNT-based electron transport. A further optimized mix of 12% LMO + 23% MWCNT (P12LM23 M) yielded 0.52 S/cm (E16), indicating synergistic effects between metal oxides and carbon nanofillers.

The highest conductivity (0.56 S/cm, E17) was observed in P15LT35 G (15% LTO + 35% GNP). This is attributed to LTO’s role in dispersing GNP uniformly and facilitating both electronic and ionic conduction, while GNP’s high conductivity enables rapid charge transfer.

In summary, GNP-based composites exhibited superior conductivity compared to CF and MWCNT-based counterparts. The integration of metal oxides (LMO/LTO) further enhanced performance via complementary conduction mechanisms, making such composites highly suitable for 3D-printed electrochemical electrodes.

Mechanical characterization

Based on optimized electrical performance, P15LT35 G was selected as the primary material for fabrication. According to supplier data, the material exhibits an extension at yield of 6.39%, tensile modulus of 40.18 MPa, melting point of 260°C, and melt flow index of 20.02 g/10 min, with a glass transition temperature of 80°C. These properties, combined with high strength and durability, make P15LT35 G well-suited for fabricating robust, high-performance components.

Sample fabrication

Test specimens were fabricated using the Fused Filament Fabrication (FFF) technique with 2.85 mm P15LT35 G filament from Rameshwaram Manufacturing Solutions. Designs followed ASTM D695 (compression), ASTM D790 (flexural), and ASTM D256 (impact) testing standards (see Figure 3(a)–(c)).

Figure 3.

Fabricated Specimen (a) Compression specimen, (b) Flexural specimen, and (c) Impact specimen.

Specimens were digitally modeled in SolidWorks and sliced in Ultimaker Cura 5.6.0, generating G-code for the Ultimaker S5 FFF printer. Critical parameters—nozzle and bed temperatures, infill density, and layer height—were optimized for consistency (details in Table 2).

Table 2.

Parameter selection.

Fixed control factors	Variable control factors
Factors	Value	Unit	Factors	Values	Unit
Nozzle temperature	240	°C	IFP	TH	--
Bed temperature	70	°C		HC	--
Infill density	80	%		GD	--
Feed rate	35	mm/s	NHD	0.15	mm
Layer height	0.2	mm		0.25	mm
Build orientation	XY	--		0.4	mm

The selection of 3D printing parameters was guided by their proven impact on mechanical strength, dimensional accuracy, and surface performance in biomedical applications. Infill pattern plays a crucial role in defining internal structure regularity and load transfer characteristics. Karadag and Ulkir³⁵ demonstrated that cubic and triangle infill patterns enhanced both surface quality and geometric precision in implants fabricated with PETG and TPU. Accordingly, grid, lines, and gyroid patterns were selected to represent orthogonal, parallel, and biomimetic structures, enabling evaluation of their influence on both mechanical response and sensor stability. The infill densities (30%, 50%, 70%) were chosen to strike a balance between structural rigidity and reduced weight, considering that higher densities improve dimensional accuracy and compressive strength but increase material usage and thermal stress during printing. Finally, nozzle diameters of 0.4, 0.5, and 0.6 mm were selected to investigate their influence on deposition fidelity and interlayer bonding, with smaller diameters providing improved resolution, consistent with the benefits observed at thinner layer settings in the cited study. All prints were oriented in the XY plane to reduce anisotropy effects. After printing, specimens were cooled to room temperature before mechanical testing.

Mechanical testing

The mechanical properties of the P15LT35 G specimens were evaluated through compression, flexural, and impact testing, following standardized procedures. A total of nine specimens were tested for each category to ensure consistency and reliability of the results.

Compression testing was conducted using an Instron 1195 universal testing machine with a maximum load capacity of 100 kN, in accordance with ASTM D695 standards. The tests were performed at a crosshead speed of 1 mm/min, and the compressive strength was calculated by dividing the maximum load by the cross-sectional area of the specimen.

Flexural testing followed ASTM D790 guidelines using a three-point bending setup. A constant loading rate of 2 mm/min was applied, and flexural strength was determined based on the span length, specimen width, and depth.

Impact strength was evaluated according to ASTM D256 using an Izod impact testing machine. Notched specimens were used to maintain consistency in stress concentration at the point of impact. The energy absorbed during fracture was measured and normalized with respect to the specimen thickness to calculate impact strength. Average values from all tests were used to assess the overall mechanical performance of the material.

Results and discussion

Mechanical performance

The mechanical properties of the P15LT35 G were evaluated by varying NHD and IFP, focusing on CS, IS, and FS. Table 3 summarizes how these parameters impact the mechanical performance of the printed samples.

Table 3.

Experimental results of mechanical testing.

NHD (mm)	IFP	Specimen code	CS (MPa)	Specimen code	IS (MPa)	Specimen code	FS (MPa)
0.15	TH	CS1	36.06	IS1	23.140	FS1	45.58
	HC	CS2	35.14	IS2	24.360	FS2	50.55
	GD	CS3	41.08	IS3	27.410	FS3	47.83
0.25	TH	CS4	39.75	IS4	24.360	FS4	53.37
	HC	CS5	37.26	IS5	25.580	FS5	55.67
	GD	CS6	44.17	IS6	32.280	FS6	52.84
0.4	TH	CS7	41.32	IS7	31.060	FS7	65.64
	HC	CS8	41.87	IS8	33.500	FS8	62.02
	GD	CS9	47.34	IS9	35.940	FS9	57.63

CS

The results indicated that an optimized NHD of 0.4 mm combined with GD IFP significantly enhanced CS, with an average CS of 47.34 MPa—confirming the structure’s ability to support user weight without deformation.

Effect of NHD

CS improved with increasing NHD. At 0.15 mm, lower values were observed — TH (36.06 MPa), HC (35.14 MPa), and GD (41.08 MPa). At 0.4 mm, CS increased notably—TH (41.32 MPa), HC (41.87 MPa), and GD (47.34 MPa), as shown in Figure 4. The improvement is attributed to enhanced layer bonding, yielding a stronger, more cohesive structure.

Figure 4.

Effect of NHD on CS: (a). Stress Strain for IFP TH, (b). Stress Strain for IFP HC, (c). Stress Strain for IFP GD, (d). CS comparision for various NHD.

Effect of IFP

IFP had a significant impact on CS, with GD consistently outperforming TH and HC across all NHD levels. At 0.15 mm NHD, GD achieved 41.08 MPa, while TH and HC recorded 36.06 MPa and 35.14 MPa, respectively. With increasing NHD, GD maintained superior performance, reaching 47.34 MPa at 0.4 mm, compared to TH (41.32 MPa) and HC (41.87 MPa). This enhancement is attributed to GD’s efficient stress distribution and strong interlayer interlocking, as shown in Figure 5.

Figure 5.

Effect of IFP on CS: (a). Stress Strain for NHD 1.15 mm, (b). Stress Strain for NHD 0.25 mm, (c). Stress Strain for NHD 0.4, (d). CS comparision for various IFP.

FS

For FS, the optimal combination of 0.4 mm NHD and TH IFP yielded an average of 65.64 MPa, indicating excellent resistance to bending forces. This ensures the socket maintains structural integrity under flexion or twisting, enhancing user comfort and reliability during movement.

Effect of NHD

FS improved significantly with increasing NHD. At 0.15 mm, FS values were 45.58 MPa (TH), 50.55 MPa (HC), and 47.83 MPa (GD). With 0.4 mm NHD, values rose to 65.64 MPa (TH), 62.02 MPa (HC), and 57.63 MPa (GD), as shown in Figure 6. This enhancement is attributed to better material distribution and improved inter-layer bonding, increasing resistance to bending forces.

Figure 6.

Effect of NHD on FS: (a). Stress Strain for IFP TH, (b). Stress Strain for IFP HC, (c). Stress Strain for IFP GD, (d). FS comparision for various NHD.

Effect of IFP

FS was also influenced by IFP, with HC and GD initially outperforming TH. At 0.15 mm NHD, FS was highest for HC (50.55 MPa), followed by GD (47.83 MPa) and TH (45.58 MPa). As NHD increased to 0.4 mm, TH showed the greatest improvement, reaching 65.64 MPa, while HC and GD reached 62.02 MPa and 57.63 MPa, respectively (Figure 7). Despite TH’s superior FS at higher NHD, HC and GD offered more uniform strength distribution, making them preferable for applications requiring structural balance.

Figure 7.

Effect of IFP on FS: (a). Stress Strain for NHD 1.15 mm, (b). Stress Strain for NHD 0.25 mm, (c). Stress Strain for NHD 0.4, (d). FS comparision for various IFP.

IS

The optimized 0.4 mm NHD combined with the “GD” IFP significantly improved impact resistance, achieving an average IS of 35.94 MPa. This indicates the socket can endure sudden shocks without cracking, ensuring long-term durability during dynamic movements.

Effect of NHD

IS, like CS, improved with increasing NHD. At 0.15 mm, IS values were 23.14 MPa (TH), 24.36 MPa (HC), and 27.41 MPa (GD). At 0.4 mm, these increased to 31.06 MPa (TH), 33.5 MPa (HC), and 35.94 MPa (GD), as shown in Figure 8. The improvement is attributed to enhanced material deposition and interlayer bonding at higher NHD, increasing resistance to impact forces.

Figure 8.

Effect of NHD on IS.

Effect of IFP

IS was also influenced by IFP, with GD consistently showing the highest values across all NHD levels. At 0.4 mm NHD, GD peaked at 35.94 MPa, followed by HC at 33.5 MPa and TH at 31.06 MPa, as shown in Figure 9. GD’s superior performance is attributed to its effective force distribution across layers, enhancing impact resistance.

Figure 9.

Effect of IFP on IS.

Statistical optimization

Statistical analysis was performed using Taguchi Methodology (TM) and Response Surface Methodology (RSM) to assess and compare the effects of process parameters on the target mechanical properties.

ANOVA with TM

To evaluate the influence of NHD and IFP on compressive, impact, and flexural strengths, ANOVA was performed for each property. The results, summarized in Table 4, include degrees of freedom (DF), sum of squares (Seq SS), adjusted sum of squares (Adj SS), adjusted mean square (Adj MS), F-value, p-value, and the percentage contribution of each factor to overall variance.

Table 4.

ANOVA.

a. Compression
Source	DF	Seq SS	Adj SS	Adj MS	F	p	Contribution
NHD (mm)	2	2.5825	2.5825	1.29125	43.38	.002	46.13%
IFP	2	2.8969	2.8969	1.44844	48.66	.002	51.75%
Residual error	4	0.1191	0.1191	0.02976			2.13%
Total	8	5.5984
S = 0.1725, R2 = 97.87%, R2 (Adj.) = 95.75%
b. Impact
NHD (mm)	2	10.3562	10.3562	5.1781	33.12	.003	65.92%
IFP	2	4.7299	4.7299	2.3649	15.13	.014	30.11%
Residual error	4	0.6253	0.6253	0.1563			3.98%
Total	8	15.7113
S = 0.3954, R2 = 96.02%, R2 (Adj.) = 92.04%
c. Flexural
NHD (mm)	2	7.1876	7.1876	3.5938	19.12	.009	86.07%
IFP	2	0.4119	0.4119	0.206	1.1	.417	4.93%
Residual error	4	0.7517	0.7517	0.1879			9.00%
Total	8	8.3513
S = 0.4335, R2 = 91.00%, R2 (Adj.) = 82.00%.

Using Taguchi’s L9 array design of experiments (DOE) and ANOVA, the study analyzes two key process variables: Infill Pattern (IFP)—tri-hexagon, honeycomb, and grid—and Nozzle Head Diameter (NHD)—0.15 mm, 0.25 mm, and 0.40 mm. The investigation focuses on the compressive strength (CS), impact strength (IS), and flexural strength (FS) of P15LT35 G. MINITAB 21 was used for statistical analysis and result evaluation.

CS

ANOVA results for CS indicate that both NHD and IFP significantly influence compressive strength, with p-values of 0.002 for each. NHD contributed 46.13% to the variance, while IFP had a slightly higher impact at 51.75%. The residual error was minimal at 2.13%, confirming a strong model fit with an R² of 97.87% and an adjusted R² of 95.75%, as shown in Table 3a. These findings confirm that both factors play a critical role in determining CS, with IFP having a marginally greater effect. SNRA and interaction plots in Figure 10 illustrate the influence and interaction of NHD and IFP on CS.

Figure 10.

SNRA and Interaction Plot showcasing the effect of NHD and IFP on Compressive Strength.

IS

ANOVA results for IS show that both NHD and IFP significantly influence impact strength, with NHD contributing 65.92% and IFP 30.11% to the variance. The p-values were 0.003 for NHD and 0.014 for IFP, confirming statistical significance. Residual error was low at 3.98%, indicating a strong model fit with an R² of 96.02% and an adjusted R² of 92.04%, as shown in Table 3b. These results highlight the dominant effect of NHD on impact resistance, with IFP also playing a notable role. SNRA and interaction plots in Figure 11 illustrate the influence of both parameters on IS.

Figure 11.

SNRA and Interaction Plot showcasing the effect of NHD and IFP on Impact Strength.

FS

For FS, NHD was identified as the most influential factor, contributing 86.07% to the total variance with a p-value of 0.009. In contrast, IFP contributed only 4.93% and had a p-value of 0.417, indicating no statistically significant effect. The residual error accounted for 9.00% of the variance. The model showed a good fit, with an R² of 91.00% and an adjusted R² of 82.00%, as presented in Table 3(c). These results suggest that FS is predominantly affected by NHD, while IFP has minimal impact. SNRA and interaction plots in Figure 12 illustrate the influence of both parameters on FS.

Figure 12.

SNRA and Interaction Plot showcasing the effect of NHD and IFP on Flexural Strength.

The statistical analysis confirms that NHD significantly influences all mechanical properties, with a dominant effect on FS and IS. IFP also contributes notably to CS and IS but has minimal impact on FS. The high R² values across all models indicate that NHD and IFP effectively account for the variations in mechanical performance, emphasizing the importance of optimizing these parameters to enhance the structural properties of the material.

ANOVA with RSM

ANOVA with RSM was conducted to assess the influence of NHD and IFP on CS, IS, and FS. The analysis quantified the contributions of linear, square, and interaction terms of both parameters on each mechanical property. The results are summarized in Table 5.

Table 5.

ANOVA with RSM results.

Source	DF	Adj SS			Adj MS		Contribution
Source	DF	CS	IS	FS	CS	IS	FS	CS	IS	FS
Model	5	120.556	167.366	330.767	24.1112	33.473	66.153
Linear	2	95.66	157.48	293.537	47.8299	78.74	146.769
NHD	1	40.149	109.141	284.641	55.5106	109.141	284.641	32.76%	62.81%	84.86%
IFP	1	55.511	48.338	8.897	40.1491	48.338	8.897	45.29%	27.82%	2.65%
Square	2	25.434	4.846	10.694	12.7168	2.423	5.347
NHD*NHD	1	0.553	1.878	0.416	0.5534	1.878	0.416	0.45%	1.08%	0.12%
IFP*IFP	1	24.88	2.969	10.278	24.8803	2.969	10.278	20.30%	1.71%	3.064%
2-Way interaction	1	0.326	0.007	27.574	0.3259	0.007	27.574
NHD*IFP	1	0.326	0.007	27.574	0.3259	0.007	27.574	0.27%	0.00%	8.22%
Error	3	2.005	6.411	4.672	0.6682	2.137	1.557	1.64%	3.69%	1.39%
Total	8	122.56	173.777	335.439
CS						S = 0.817419, R² = 98.36%, R²(adj) = 95.64%
IS						S = 1.46180, R² = 96.31%, R²(adj) = 90.16%
FS						S = 1.24792, R² = 98.61%, R²(adj) = 96.29%

To evaluate the influence of NHD and IFP on mechanical performance, ANOVA using RSM was conducted. The contributions of linear, square, and interaction terms were analyzed for CS, IS and FS. The regression equations and model accuracies are summarized below.

For CS, the model showed an R² of 98.36% (eq. (1)) and an adjusted R² of 95.64%, indicating strong predictive accuracy. Linear terms of NHD and IFP contributed 32.76% and 45.29% respectively, while the IFP² term had a notable impact (20.30%). The NHD*IFP interaction was minimal (0.27%), and error was low (1.64%).

CS (MPa) = 39.48 + 39.2 NHD ‐ 12.14 IFP ‐ 35.3 {NHD}^{2} + 3.527 {IFP}^{2} + 2.27 NHD * IFP \dots

(1)

For IS, the model yielded an R² of 96.31% (eq. (2)) and an adjusted R² of 90.16%. NHD had the highest contribution (62.81%), followed by IFP (27.82%). Square terms had minor effects: IFP² (1.71%) and NHD² (1.08%). The interaction term had negligible impact (0.00%), and residual error was 3.69%.

IS (MPa) = 22.30 + 2.3 NHD ‐ 2.11 IFP + 65.0 {N H D}^{2} + 1.221 {IFP}^{2} + 0.32 NHD * IFP \dots

(2)

For FS, the model achieved R² of 98.61% (eq. (3)) and adjusted R² of 96.29%. NHD contributed 84.86%, making it the most influential factor. IFP had a minor effect (2.65%), while square terms IFP² and NHD² contributed 3.06% and 0.12% respectively. The NHDIFP interaction had a moderate impact (8.22%). Error was minimal at 1.39%.

FS (MPa) = 21.30 + 113.7 NHD + 13.58 IFP ‐ 30.6 {N H D}^{2} ‐ 2.267 {IFP}^{2} ‐ 20.87 NHD * IFP \dots

(3)

These results confirm that NHD is the dominant parameter influencing all three mechanical properties, with IFP contributing significantly to CS and IS, and having limited effect on FS.

Surface and contour plots (Figure 13(a)–(c)) were used to visually assess the interactive effects of process parameters on CS, IS, and FS, highlighting how these properties vary with changes in NHD. Among IFPs, grid pattern yielded the highest CS. The surface response plots, derived from the regression equations, illustrate these trends, while Figure 14(a)–(c) compare experimental and predicted values, providing insight into parameter interactions.

Figure 13.

Surface and Contour plots for CS, IS, and FS.

Figure 14.

Radar Chart for experimental and RSM Predicted Values of (a). CS, (b). IS and (c). FS.

Overall, ANOVA with RSM confirmed that NHD is the dominant factor influencing all mechanical properties, particularly FS and IS. IFP significantly affects CS and IS but has minimal impact on FS. Interaction effects were generally minor, except for FS, where the NHD*IFP interaction contributed notably. High R² values and low residual errors across all models validate the effectiveness of NHD and IFP in explaining performance variations, emphasizing their optimization for improved material performance.

Figure 14(a)–(c) present the results obtained from equations (3)–(5) for CS, IS, and FS, respectively. These plots confirm the high reliability and accuracy of the ANOVA with RSM model, showing strong alignment between experimental and predicted values. The close correlation highlights the robustness and predictive capability of the developed model.

Fabrication of the Prosthetic

The design of the strain-sensing prosthetic socket is such that the embedded sensor is neither visible on the inner nor outer surface of the prosthetic socket. However, the outer surface of the socket gives openings for the sensor to transmit the strain signals. Figure 15 provides a pictorial representation of the designed PETG prosthetic socket, embedded with P15LT35 G strain sensor as an integral part. Fabrication was performed on an Ultimaker S5 printer using 2.85 mm P15LT35 G filament, printed in XY orientation to minimize anisotropy. The process took approximately 16 h, with only minor post-processing (light sanding) required for surface finishing.

Figure 15.

Prosthetic socket with inner and outer cladding fabricated out of PETG.

After wearing the prosthetic liner, the amputee wears the prosthetic socket which is attached with the prosthetic limb. This means that the main load of the amputee is born by the prosthetic socket. The strain sensor is embedded as such that notwithstanding the size and the shape of the amputation, the sensor is able enough to sense the strain wherever the loading occurs. This can be better explained with the pictorial representation displayed in Figure 16. Outer cladding of PETG is absent in the figure and thus it completely brings out the design of the embedded strain sensor.

Figure 16.

Prosthetic socket without outer cladding.

Based on the experimental results and the statistical analysis, the optimal configuration, to be implemented for the fabrication using P15LT35 G, was decided. A 0.4 mm NHD ensured precise material deposition, while the GD IFP provided structural integrity with reduced material usage. An infill density of 60% and layer height of 0.2 mm offered optimal rigidity, surface quality, and mechanical performance. Printing was conducted at 240°C nozzle and 70°C bed temperatures, consistent with earlier test conditions. Wall thickness was optimized to 5 mm, with reinforced zones added in load-bearing areas, and ventilation holes included to improve comfort and airflow. Keeping these parameters in position, the whole prosthetic socket is fabricated out of PETG, and the sensor is embedded out of P15LT35 G as shown in Figure 17. This PETG-based composite material offers a durable, efficient, and high-performance strain sensor, ideal for force sensing in prosthetic sockets. The optimized composite was successfully incorporated into a 3D-printed prosthetic socket, enhancing pressure distribution, structural durability, and personalized fit.

Figure 17.

Fabricated Prosthetic Socket with embedded strain or force sensor.

The developed prosthetic socket, as illustrated in Figure 17, functions as the critical interface between the prosthetic liner, holding patient’s residual limb and the rest of the prosthetic leg assembly. Custom-designed through patient-specific 3D scanning and CAD modeling, the socket is fabricated to ensure an optimal, secure, and comfortable fit. Embedded within the structural walls of the socket is a strain sensor made from the conductive PETG-based composite P15LT35 G. This sensor is strategically located in load-bearing regions where peak stresses are anticipated during ambulation, thereby providing continuous real-time monitoring of strain distribution across the socket-liner interface. Integrated electronics capture and relay sensor data to a portable receiver, enabling clinicians or the patient to assess interface pressures and detect early signs of misalignment or excessive loading that might compromise comfort or tissue health. Furthermore, the socket design features standard mechanical coupling interfaces at its distal end to ensure robust attachment to the prosthetic pylon, allowing the assembly to withstand repeated cyclical loading without compromising structural integrity. This multifunctional design not only provides structural support but also offers a smart, feedback-enabled interface, laying the foundation for adaptive prosthetic systems that can dynamically monitor the user’s activity and physiological changes.

Sensor Characterization

To assess the performance of the 3D-printed strain sensor developed using P15LT35 G, a series of controlled tensile tests were conducted as shown in Figure 18. P15LT35 G, being a thermoplastic composite, exhibits inherently low piezoresistive sensitivity, which aligns well with the intended application in prosthetic sockets. During testing, the sensor was subjected to incremental strain levels from 0% to 10%, and the corresponding resistance was recorded in real time as shown in Figure 19. The sensor’s electrical response was characterized by the relative change in resistance (ΔR/R₀), where R₀ denotes the initial resistance. The resulting ΔR/R₀ vs. strain behaviour demonstrated a smooth, nonlinear increase, accurately modelled using a second-order polynomial:

\frac{∆ R}{R} = α ε + b ϵ^{2}

with coefficients

α

= 1.5 and b = 4.0. This low-sensitivity profile is particularly advantageous for prosthetic applications, where moderate, distributed interfacial stresses occur during daily activities such as walking or sitting. It ensures stable, repeatable measurements without signal saturation, enabling effective tracking of pressure distribution at the limb–socket interface. The test results confirm that the conductive PETG-based sensor is suitable for integration into prosthetic systems aimed at improving comfort and preventing pressure-related injuries.

Figure 18.

Sensor testing setup.

Figure 19.

Strain applied versus change in resistance.

Discussion

This study demonstrated the fabrication and characterization of a piezoresistive strain sensor integrated into a 3D-printed prosthetic socket using a conductive PETG-based composite (P15LT35 G). The ΔR/R₀ response of the sensor showed a nonlinear yet stable behavior, best fitted by a second-order polynomial, with a measured gauge factor (GF) of approximately 1.5. This moderate sensitivity aligns well with the mechanical and practical requirements of prosthetic applications, where distributed stress sensing and long-term signal stability are prioritized over high-resolution detection.

In comparison, Gunes et al. (2025)³⁶ developed a highly flexible strain sensor using a TPU substrate and liquid silver conductive paths, reporting a GF of 1.66 and a nearly linear resistance-strain curve up to 30% strain. Their sensor was designed for flexibility and high sensitivity, achieving a 49.85% resistance change at maximum extension, with minimal hysteresis. While their configuration is ideal for applications requiring fine strain resolution, the use of soft materials and separate molding steps may compromise mechanical durability and long-term integration in load-bearing systems.

By contrast, our approach integrates sensing and structural functionality into a single-material socket, using an FDM-compatible composite filament, simplifying fabrication and enhancing mechanical robustness. However, limitations such as nonlinear output, potential drift under cyclic loading, and limited dynamic range still exist. These are common to thermoplastic-based sensors and must be addressed through further cyclic fatigue testing, temperature sensitivity studies, and real-world validation under daily-use prosthetic conditions.

Despite the trade-offs in sensitivity, the developed sensor offers practical advantages for embedded prosthetic monitoring, with repeatable electromechanical performance and direct compatibility with fused filament fabrication. This work contributes to the growing field of structurally integrated, additively manufactured sensing systems and establishes a foundation for future clinical translation.

Conclusion

This study successfully developed a universal 3D-printed prosthetic socket embedded with a strain sensor, designed to enable real-time monitoring of stress distribution and pressure points for enhanced user comfort and safety. A conductive PETG-based composite (P15LT35 G: 15% LTO + 35% GNP) was selected for its favorable electromechanical properties, and its mechanical performance was validated through compression, impact, and flexural strength testing, confirming its suitability for load-bearing prosthetic use. Fabrication was optimized using ANOVA to fine-tune critical printing parameters, including nozzle hole diameter and infill pattern. A full factorial design (3³) and RSM-based modeling confirmed the significant influence of nozzle hole diameter, infill pattern, and density on mechanical and sensing performance. The optimized socket configuration demonstrated excellent structural integrity (25.62 MPa compressive strength) and reliable sensor output with a gauge factor of 1.52 and nonlinearity of 4.01. The integrated sensor exhibited a low-sensitivity, nonlinear piezoresistive response under tensile loading, aligning well with the moderate and distributed stresses encountered during everyday prosthetic use. By demonstrating stable and realistic sensor behavior within a functional socket structure, this work highlights the viability of embedding conductive composites into prosthetic systems, offering a promising path toward smart, adaptive, and personalized prosthetic solutions.

Moving forward, the integration of the developed sensor-embedded socket in real-world prosthetic systems requires further validation through in vivo testing and user-specific trials to assess comfort, mechanical fatigue, and sensor drift under daily use conditions. Additionally, coupling the printed conductive paths with low-power wireless electronics such as Bluetooth-enabled microcontrollers can facilitate real-time monitoring of socket-limb interactions, enabling early detection of socket misfit or excessive loading. This lays the groundwork for future development of intelligent prosthetic sockets capable of autonomous feedback-driven adjustments, either through mechanical actuators or thermally responsive materials. To translate this research into scalable clinical solutions, robotic deposition systems and multi-head 3D printers can be explored for automated, high-precision fabrication of socket geometries with embedded functional zones. These advancements have the potential to bridge the gap between bespoke prosthetic design and industrial-level production.

Footnotes

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.

ORCID iDs

Abhishek Raj

Ankit Sahai

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Optimization of conductive PETG-based composite for strain-sensing prosthetic sockets using 3D printing

Abstract

Keywords

Introduction

Materials and Methods

Materials

Followed methodology

Fabrication of filament materials

Electrical conductivity

Mechanical characterization

Sample fabrication

Mechanical testing

Results and discussion

Mechanical performance

CS

Effect of NHD

Effect of IFP

FS

Effect of NHD

Effect of IFP

IS

Effect of NHD

Effect of IFP

Statistical optimization

ANOVA with TM

CS

IS

FS

ANOVA with RSM

Fabrication of the Prosthetic

Sensor Characterization

Discussion

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iDs

References