A Novel Model for Computing D-Shore Hardness of PLA: Numerical and Experimental Investigation

1. Introduction

In the preliminary design stages for various fields, such as construction, automobile, marine, and aerospace, the modeling operation has employed 3D printing technology [1,2,3]. The advanced and precise manufacturing of human body parts in the biomedical area, especially bones and teeth, has also utilized this technology [4,5,6,7]. Therefore, earlier studies aimed to develop this industry using distinct kinds of filaments, such as polylactic acid (PLA) [8,9]. At the same time, the porosity mechanism is considered one of the revolutionary techniques for enhancing biomedical parts as functional materials, yielding better economic and lower weight patterns [10,11].

Given the preceding, the bio-fabrication field of utilizing PLA for bone and teeth has undergone significant advancements due to the unique features of this type of aliphatic polyester, such as biodegradability and recyclability. Furthermore, this type of filament is eco-friendly and non-toxic because it is fermented from the sugar of sugarcane and corn. Accordingly, the tissue engineering of bones is deemed one of the essential applications of this filament type [12,13,14]. Thus, the Fusion Deposition Modeling (FDM), as a mechanism employed in 3D printers, has been exploited in the scaffolds modeling for bone tissue, where one of these models proposed a regular porosity from 200-350 μm and 90% porosity grade to boost the resurgence of the bone tissues without mechanical properties issues [15]. Additionally, this filament can provide osteogenic properties to healing and implantation. As a testament to these properties, this printed filament successfully eliminated damage to bone tissue in the cortical skull bones of mice. Therefore, the size of the pores in the implanted scaffolds in this bone for the mice ranged from 250 to 1000 μm with a variance in orientation angles from 0˚ to 28˚ [16]. However, other studies have employed a dis-tinct pore size of approximately 100 μm in the fabrication of bone from a ceramic matrix composite and polyurethane [17,18,19]. Consequently, this brief survey has shown the influential function of PLA filament in this medical field. Nonetheless, this filament has limited toughness, since it tends to be brittle [20]. Accordingly, it is essential to comprehend the role of other parameters in enhancing the hardness of bones fabricated, after focusing on the pore size range in bone microfabrication using PLA.

The numerous parameters of FDM weigh on the performance of indentation resistance as a function of PLA hardness. Hence, the thickness and orientation of layers, nozzle temperature, the ratio of infill density, and printing speed are influential parameters in improving this type of resistance [21,22,23]. One of these experimental investigations on this type of filament demonstrated the influence of a 0.1 mm layer height on enhancing hardness, as measured by the D-Shore method at 45˚/-45˚ [24]. Nevertheless, the horizontal and vertical orientation of the printed layers, with a height of 0.15-0.20 mm for each layer, contributed to the increase and stability of PLA hardness [25]. Moreover, the dominance of extrusion temperature compared to infill density and printing speed led to variance in the optimization of hardness behavior. Therefore, the optimal outputs for this experimental procedure were 100%, 220˚C, and 20 mm/s for infill ratio, nozzle temperature, and printing velocity, respectively [26]. In addition, this optimization variance for PLA hardness also presented other reported outcomes represented by 0.25 mm, 65%, and 215˚C for layer height, infill ratio, and extrusion temperature of the nozzle, consecutively [27]. In contrast, the Brinell hardness method was employed with other filament types, as compared to PLA, which usually utilizes the D-Shore method to measure hardness [28]. According to this concise review, the vital levels of key factors affecting the hardness of PLA filament and the pore sizes of bone fabricated from this filament can be summarized in Figure 1.

From here, the synopsis in Figure 1 provides a comprehensive overview of the influential ranges of parameters for boosting this type of fabrication by modifying the indentation resistance and pore sizes of PLA filaments. Similarly, this synopsis demonstrated that PLA filaments were used in conjunction with the D-Shore technique to measure hardness, whereas the Brinell method was employed with other types of filaments [28]. Furthermore, the Brinell method is a widely used test that employs a mathematical formula, unlike the D-Shore method [29,30]. Therefore, the current study focuses on utilizing a variety of micropore sizes and layer orientations to investigate numerically and experimentally the best level of hardness of the PLA sample. Accordingly, by applying the Brinell and D-Shore examinations' outcomes to the PLA samples, these results contribute to establishing a novel D-Shore model. Methodologically, PLA filament is operated at 20 mm/s, 220˚C, 0.2 mm, and 100% for the printing speed, nozzle temperature, layer thickness, and infill ratio, successively. The angles of orientation layers are 0˚/90˚ and 45˚/-45˚, while the micro-sizes for the pore are 100, 150, and 200 μm. Predictively, the indentation’s load is applied to PLA samples using the Explicit Finite Element Analysis (EFEA) technique to determine the Brinell hardness. Thus, this prediction can specify the range of affording for proposed structures of samples to indentation. Based on this concise presentation of methodology procedures, the adopted prediction environment for hardness in this work, along with the experimental settings, contributes to illustrating the numerical and experimental aspects of the current study in succession.

2. Materials and Methods

2.1. Hardness Prediction Environment

Since the data available on the strength of this filament type is scarce, the simulation challenge of indentation behavior for Micro-Samples of PLA utilizing EFEA is complex [31,32]. Furthermore, the sample structure needs to predict the feasibility of the orientation angles of layers and pore sizes adopted in the current work before executing the experimental trials to avoid wasting this filament type [33,34,35]. Therefore, it is essential to demonstrate the Johnson-Cook model's role in describing the behavior of indentation resulting from stressed PLA samples by the Brinell hardness method.

As a concept, the ball tool in the Brinell hardness method begins to penetrate the PLA sample surface to measure the strength of this filament type under indentation, as depicted in Figure 2 [29]. Hence, the nonlinear strength behavior of PLA material in Equations (1) and (2) lead to access to explicit deformation resulting from applied load during this hardness test. This deformation resulting from the penetration of the ball tool contributes to the strain of the PLA surface with increasing penetration depth, as described in Equation (3) [31,36].

$$F_i=m\left({{\delta }_i}^{n+1}-{{\delta }_i}^{n+0.5}{∆t}^{n+0.5}-a_i\right),$$

(1)

$${{\delta }_i}^{n+1}={{\delta }_i}^n+{{\delta }_i}^{n+0.5}{∆t}^{n+0.5},$$

(2)

$${\epsilon }_{\delta }={∆h}_{\delta }/h,$$

(3)

where F_i is the nodal applied force, δ_i is the final nodal acceleration, a_i indicates the acceleration of the body, Δt is the incremental time, m is the nodal mass, n is the iteration number, ε_δ is the directional strain, and h denotes the nodal indentation. Consequently, the applied force in this hardness method on the indentation tool contributes to the interaction between directional strain and the kinetic energy, where this interaction reflects the decrease in tool penetration inside the sample, which can be observed in Equation (4):

$$I_k=0.5m\left({∆v\epsilon }_{\delta }\right),$$

(4)

where Δv is the variance among the initial and final velocities for the hardness tool according to the Brinell test, this variance represents the progress of deformation between elements based on augmented Lagrange's principle. Hence, this progress needs time, based on a scale of mass density (ρ) and Young's modulus (E) for PLA filament, as illustrated in Table 1. Mesh size (S) and factor of safety (f.o.s), according to EFEA, are also required in progressive deformation. Thus, it can translate these factors into the Courant-Friedrichs-Lewy (CFL) in Equation (5), where the value of f.o.s is ≤ 1. At the same time, the properties of Tungsten Carbide (WC) are also stated in Table 1 for the ball tool.

$$∆t\le f.o.s{\left[S/\sqrt{E/\rho }\right]}_{min},$$

(5)

Through this brief explanation of explicit deformation formulas resulting from PLA indentation by a ball tool, the strength model adopted in the present EFEA simulation relies on the Johnson-Cook (JC) model. Therefore, this model interprets the strength of PLA filament opposite this indentation to obtain the indentation diameter, as demonstrated in Figure 2(a). At room temperature, the assumed PLA strength of this model in the current study can be applied without considering the temperature influences, as exhibited in Equation (6) [39]:

$${\sigma }_{JC}=\left(k+N{ϵ}^x\right)\left[1+R\ln \left(\dot{ϵ}/\dot{{ϵ}_o}\right)\right],$$

(6)

where σ_JC is the stress according to the JC-Model, k indicates the initial yield stress, N is the strength coefficient, x is the strain hardening exponent, and R signifies the strain rate strength coefficient. These constants of Equation (6) can be seen in Table 2 for PLA filament at orientation angles 0˚, 45˚, and 90˚. Moreover, the reference strain rate ($\dot{{ϵ}_o}$) is one unit, while $ϵ$ and $\dot{ϵ}$ are the equivalent plastic strain and plastic strain rate, respectively.

As mentioned, the basis adopted for the plastic deformation of PLA filament in this study is nonlinear behavior according to the augmented Lagrange and EFEA principles, as described in Equations (1)-(6). Therefore, the traditional version of SOLIDWORKS 2025, as a CAD tool, has modeled the PLA micro-samples depicted in Figure 3 for exploitation in the simulation operation. Moreover, as a subsequent step in the experimental procedures, 3D printing was utilized to prepare these samples for the Brinell and D-Shore hardness testing. On the other hand, the simulation of these samples in Figure 3 was achieved using a traditional version 6.1 of the Solid Mechanics Package-Time Dependent in COMSOL Multiphysics. One of these meshed samples at 0˚/90˚ and (100×100) μm² for the orientation layers and pore size, respectively, can be seen in Figure 4.

As is apparent from the facts outlined above, the following section focuses on highlighting the experimental surroundings for implementing the printing of these micro-samples and conducting the hardness tests, after describing the prediction environment of the indentation situation.

2.2. Experimental Surrounding

In the present work, the prediction medium of the penetration process during the Brinell test has become apparent based on principles of EFEA and nonlinear behaviors. Accordingly, it is essential to ascribe this test, along with the D-Shore method, to specify the hardness of these Micro-Samples, depending on the methodological path adopted in the experimental surroundings. Therefore, this surrounding comprises the adopted parameters, the parameters' levels, the specifications of 3D printing, and the hardness test instruments. Consequently, it is noteworthy to highlight these experimental procedures.

Based on the graphical summary of the survey in Figure 1, the influential pore sizes (PS) used in the current study were 100, 150, and 200 μm, while (0˚/90˚) and (-45˚/45) were the angles for the orientation layer (OL), as shown in Table 3. On the contrary, the other parameters in Table 4 utilized to model the Micro-Samples depicted in Figure 3 can be recognized as operational specifications in a 3D printer model (Cocoon Create, Australia) that were constant. In tissue engineering, the main reason for selecting these PS levels is to promote absorption and adhesion to protein and cells, respectively, at the early phase of these sizes. Besides, these active levels of PS contribute to increasing the rate of bone reconstruction as a bionic trabecular structure. These dimensions also ensured optimal exchange and growth for both nutrients and blood vessels, individually. Likewise, these PS levels increase bone porosity by 50% to 80%. Hence, it enhances the structural flexibility and the mechanical strength of bone [41,42,43,44,45,46,47]. In addition, as illustrated in Table 4, the filament material was a black PLA model (Hatchbox, USA) with a diameter of (1.75) mm, (+/- 0.03) mm for accuracy in dimensions, and 1 kg for weight. Accordingly, the levels of PS and OL in Table 3 were designed for 12 trials, using both non-hybrid and hybrid pore sizes, as demonstrated in Table 5, to measure the hardness.

According to the prediction environment for hardness and the number of hardness resulting from the Brinell method [29], as illustrated in Equation (7), the numerical prediction of this number is implemented based on the trials presented in Table 5.

$$HB=0.204F/\pi D\left(D-\sqrt{D^2-d^2}\right),$$

(7)

where F is the applied force on the ball tool, D is the ball diameter, and d indicates the indentation diameter. Nevertheless, the experimental measurement for HB and HS numbers according to Brinell and D-Shore, respectively, can be specified using a multifunctional instrument model (UT347A Leeb, Singapore). From here, the methodological stages adopted in the present study are illustrated in Figure 5, which includes the 3D printing stage for the Micro-Samples described in Figure 3 and the hardness measurement stage for the trials presented in Table 5.

This succinct depiction finally presented the notion of experimental surroundings adopted. Therefore, the scenario of this environment contributes to the investigation, debate, and interpretation of the outcomes in the next section. Thus, the outputs of this methodology lead to proposing the model for D-Shore based on the Brinell hardness number.

3. Results and Discussion

The description of the prediction and experimental environments provided a brief explanation of the methodology employed in this study to determine the numerical value for hardness based on the Brinell method. Furthermore, this methodology contributes to specifying the experimental hardness numbers for the Brinell and D-Shore. From here, it is indispensable to show these outcomes and examine the behavior of these results to identify the dominant parameters and the empirical model for D-Shore based on the Brinell number.

Predictively, the simulation of the Brinell environment outlined the indentation zones in run Nos. 1 and 4, as comparative samples for EFEA simulation in Figure 6. Depending on the concept of the Brinell method demonstrated in Figure 2, it is essential to pinpoint the ball and indentation diameters at each run reported in Table 5. Accordingly, the standard ball diameter utilized in the experimental Brinell and D-Shore methods was 2.3813 mm. Additionally, the measurement time applied at each trial typically was 0.5 s for these samples. Therefore, the indentation radius can be predicted, as illustrated in Figure 6. Hence, the resulting diameters from the numerical and experimental at each run can measure the Brinell hardness number described in Equation (7).

In Table 6, the predictive and experimental data reflected the reality of validation for HB numbers, and the error ratios did not exceed 6% for all trials. In prior studies of bone fabrication [48,49,50], the test methodology for mechanical properties depended on checking the structural integrity and accuracy of pores in bone scaffolds using optical microscopy before these tests. These studies have shown a slight discrepancy in dimensions between CAD models and real samples, where the consistency of flow rate, melt viscosity, and thermal shrinkage for PLA filaments during the 3D printing deposition operation is slightly fluctuating [51,52,53,54,55]. Therefore, these limitations related to thermal deposition in additive manufacturing technology contribute to this discrepancy, resulting in error ratios between predicted and experimental HB values of less than 6%. Consequently, the symmetrical model adopted in EFEA for HB is feasible and can predict the strength behavior against the indentation for PLA samples. Accordingly, the predictive environment played a significant role in demonstrating the viability of these designed samples, illustrated in Figure 3, in the experimental medium. As depicted in Figure 6, the predicted outputs of HB numbers for trials 1 and 4 have approached the experimental outcomes at (100×100 μm²) of pore size, where the error ratios illustrated in Table 6 for these trials were not over 5% and 2%, respectively. On the other hand, the average hardness numbers produced by the D-Shore method for runs 1 and 4 in Table 7 were 92.98 and 147.83, respectively. However, what's important is that the leap of HB and HS numbers in Table 6 and Table 7 increased by 125.489% and 58.991% for these trials sequentially. This leap in these outcomes, as described in Figure 7, was a result of employing -45˚/45˚ for odd and even layers in Micro-sample No. 4 instead of 0˚/90˚, since this OL at -45˚/45˚ can efficiently analyze and reduce plastic strain during this hardness test compared to 0˚/90˚ [56,57].

The non-hybrid pore sizes employed in trials from (1) to (6), as illustrated in Table 6 and Table 7 and Figure 7, revealed that the OL parameter played a less essential role for HB and HS numbers at 0˚/90˚ compared to -45˚/45˚. Simultaneously, the hardness number depending on the Brinell and D-Shore methods at the size of the hybrid pores for runs from (7) to (12) has a similar behavior to trials No. 1-6, especially at -45˚/ 45˚. Nonetheless, the size of pores in hybrid run 10 had less influence on HB and HS numbers compared to trial 4, as depicted in Figure 7, at -45˚/45˚. The main reason for this behavior is attributed to the homogeneity of pore sizes in the non-hybrid case for run No. 4. Consequently, the concentration of porosity density in these samples is lower [58,59,60]. In contrast, the values of HB and HS for trials No. 1 and 7 have a slighter effect at 0˚/90˚ than trials No. 4 and 10. According to the Analysis of Variance (ANOVA) illustrated in Table 8 and Table 9, the size of the pores in the trials conducted is a non-significant parameter in the Brinell and D-Shore tests, while the OL-Parameter is dominant in these runs. Given these facts, trial No. 4 is considered the best outcome for HB and HS at 100×100 μm² and -45˚/45˚ for OL and PS, respectively, where this design supplies a lower intensity of porosity with the ability to reduce the indentation force at angles -45˚/45˚. Therefore, the outcomes of ANOVA, besides the behavior of Micro-Samples, indicate that the increased pore sizes over 100×100 μm² in non-hybrid and hybrid cases lead to a lowering of the dominance of the PS parameter in the current work. Casually, the strength in these samples is insufficient to resist the indentation resulting from the hardness tool [61,62].

Depending on the experimental outcomes, the fitting function for the D-Shore hardness number (HS) based on the number of Brinell hardness (HB) is:

$$HS=A{e}^{QHB},$$

(8)

where A and Q are the empirical constants related to the experimental data of hardness numbers (HS) and (HB) relying on OL and PS parameters operated in the present work. Accordingly, both sides of Equation (8) apply the logarithmic rule to determine these empirical constants, as follows [63]:

$$\ln HS=\ln A+QHB,$$

(9)

Then, the fitted values are:

$$A=\exp \left(a\right)=\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n}\ln {HS}_i{\displaystyle {\sum }_{i=1}^n}{{HB}_i}^2-{\displaystyle {\sum }_{i=1}^n}{HB}_i{\displaystyle {\sum }_{i=1}^n}{HB}_i\ln {HS}_i}{n{\displaystyle {\sum }_{i=1}^n}{{HB}_i}^2-{\left({\displaystyle {\sum }_{i=1}^n}{HB}_i\right)}^2}}\right),$$

(10)

$$Q=q={\displaystyle \frac{n{\displaystyle {\sum }_{i=1}^n}{HB}_i\ln {HS}_i-{\displaystyle {\sum }_{i=1}^n}{HB}_i{\displaystyle {\sum }_{i=1}^n}\ln {HS}_i}{n{\displaystyle {\sum }_{i=1}^n}{{HB}_i}^2-{\left({\displaystyle {\sum }_{i=1}^n}{HB}_i\right)}^2}},$$

(11)

It is better to minimize Equation (8) to avoid unfitted values of HB and HS numbers as observed:

$${\displaystyle {\sum }_{i=1}^n}{HS}_i{\left(\ln {HS}_i-a-Q{HB}_i\right)}^2,$$

(12)

Based on the least squares fitting rule, then Equation (12) yields:

$$a{\displaystyle {\sum }_{i=1}^n}{HS}_i+q{\displaystyle {\sum }_{i=1}^n}{HB}_i{HS}_i={\displaystyle {\sum }_{i=1}^n}{HS}_i\ln {HS}_i,$$

(13)

$$a{\displaystyle {\sum }_{i=1}^n}{{HB}_{i}HS}_i+q{\displaystyle {\sum }_{i=1}^n}{{HB}_i}^2{HS}_i={\displaystyle {\sum }_{i=1}^n}{{HB}_{i}HS}_i\ln {HS}_i,$$

(14)

$$\left[\begin{array}{cc}{\displaystyle {\sum }_{i=1}^n}{HS}_i& {\displaystyle {\sum }_{i=1}^n}{HB}_i{HS}_i\\ {\displaystyle {\sum }_{i=1}^n}{{HB}_{i}HS}_i& {\displaystyle {\sum }_{i=1}^n}{{HB}_i}^2{HS}_i\end{array}\right]\left[\begin{array}{c}a\\ q\end{array}\right]=\left[\begin{array}{c}{\displaystyle {\sum }_{i=1}^n}{HS}_i\ln {HS}_i\\ {\displaystyle {\sum }_{i=1}^n}{{HB}_{i}HS}_i\ln {HS}_i\end{array}\right],$$

(15)

Finally, the fitted values of the constants A and Q are:

$$A=\exp \left(a\right)=\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n}\left({{HB}_i}^2{HS}_i\right){\displaystyle {\sum }_{i=1}^n}\left({HS}_i\ln {HS}_i\right)-{\displaystyle {\sum }_{i=1}^n}\left({{HB}_{i}HS}_i\right){\displaystyle {\sum }_{i=1}^n}\left({{HB}_{i}HS}_i\ln {HS}_i\right)}{{\displaystyle {\sum }_{i=1}^n}{HB}_i{\displaystyle {\sum }_{i=1}^n}\left({{HB}_i}^2{HS}_i\right)-{\left({\displaystyle {\sum }_{i=1}^n}{{HB}_{i}HS}_i\right)}^2}}\right),$$

(16)

$$Q=q={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n}{HS}_i{\displaystyle {\sum }_{i=1}^n}\left({{HB}_{i}HS}_i\ln {HS}_i\right)-{\displaystyle {\sum }_{i=1}^n}\left({{HB}_{i}HS}_i\right){\displaystyle {\sum }_{i=1}^n}\left({HS}_i\ln {HS}_i\right)}{{\displaystyle {\sum }_{i=1}^n}{HB}_i{\displaystyle {\sum }_{i=1}^n}\left({{HB}_i}^2{HS}_i\right)-{\left({\displaystyle {\sum }_{i=1}^n}{{HB}_{i}HS}_i\right)}^2}},$$

(17)

Thus, the coefficients A and Q of the D-Shore hardness number in Equation (8) for non-hybrid and hybrid pore sizes cases in Table 8, depending on the number of Brinell, describe the outcomes of Equations (16) and (17) consecutively.

According to these results, the empirical model of the D-Shore number in Equation (8) is deemed a novel model output based on HB numbers, where the correlation factor (R²) for this model, as demonstrated in Table 10, has ranged from 0.9955 to 0.9999. In the tissue engineering of bones, as a practical application, this model can be utilized to estimate the hardness of biomedical parts fabricated from PLA filaments [64,65,66]. Moreover, the experimental results presented in this study demonstrated that the size of the minimum pores in the non-hybrid style at -45˚/45˚ is beneficial for this novel model, as the lower porosity concentration contributes to enhancing the strength of the PLA surface against indentation [61]. As the scope of future work, this model can be improved by incorporating a variety of pore shapes and filament types in the biomedical fabrication fields (61,62) [67,68].

5. Conclusions

The porosity in the microfabrication is a promising area in developing bone tissue modeling. Therefore, this article adopted a regular distribution of non-hybrid and hybrid dimensions for micro-pore sizes of PLA samples. These samples consist of 12 layers with orientation angle (0˚/90˚) or (-45˚/45˚), where these pores are distributed at each layer. Hence, the current study aimed to design a feasible approach against the indentation for each sample based on the principles of Explicit Finite Element Analysis (EFEA). The experimental outcomes of Brinell and D-Shore hardness numbers were also utilized to develop a novel mathematical model for D-Shore hardness, based on these results. Consequently, the present study concluded the following:

• The predictive environment using EFEA bases contributed to specifying a feasible design for the Micro-Samples against the indentation force. The best samples for 0˚/90˚ and -45˚/45˚ were at trials Nos. 1 and 4, respectively. Whereby the Brinell hardness numbers were 18.12 and 41.99 consecutively. Experimentally, the estimated values of HB were 18.91 and 42.64 for these runs. Hence, the error ratios for these experiments did not exceed 5% and 2% successively.
• The orientation layers for the printed Micro-Sample at -45˚/45˚ rather than 0˚/90˚ effectively enhanced the analysis of indentation force and reduced plastic strain in trial No. 4. As a result of this behavior, the average number of HS based on the D-Shore method increased from 92.98 to 147.83, by 58.991% for runs Nos. 1 and 4 sequentially. On the other hand, the growth ratio of HB was 125.489% based on the expansion in HB number from 18.91 to 42.64 for trials Nos. 1 and 4, respectively.
• The orientation layers according to ANOVA are the dominant factor in the Micro-samples, while the pore sizes at (100×100 μm2), as a feasible parameter in the tissue's pore design, lost their dominant role over this size. The main reason for this behavior is attributed to the increased porosity percentage in these samples, which contributes to reducing the resistance of the sample surface against the indentation force of the hardness tool.
• The proposed model for D-Shore hardness, a novel model based on the experimental results of HB and HS numbers, has boasted a correlation rate from 99.55% to 99.99%. Consequently, this model can measure the number of D-Shore hardness using the Brinell method only for PLA samples with various fields, especially in the bone- biomedical area.

Relying on these truths to enhance the resistance of indentation, this article encourages that the pore of tissue design must not exceed (100x100 μm²). Likewise, the orientation layers for bone fabrication must employ (-45˚/45˚). Similarly, the main recommendation is to employ the novel model of D-Shore produced from this study to measure the hardness of PLA samples based on HB numbers. Therefore, it can utilize these outcomes in tissue engineering applications for bone fabrication, with the ability to employ different types of filaments and other shapes for the tissue's pores.