Abstract
Porous PLA-based bone scaffolds with tailored lattice architectures are increasingly investigated for biomedical applications due to their potential to mimic the mechanical behavior of trabecular bone. The novelty of this study lies in systematically comparing FCC, RF, and OT lattice geometries using PLA, identical FDM process parameters, unit-cell dimensions and strut diameter, and compression test conditions. Scaffolds were fabricated via Fused Deposition Modeling (FDM) and evaluated through finite element simulations and compression tests. Pore densities were 55.72% (FCC), 72.62% (RF), and 85.68% (OT), within the reported range of human trabecular bone. Experimental compressive modulus values were 192.186 MPa (FCC), 97.418 MPa (RF), and 62.162 MPa (OT), demonstrating strong topology-dependent mechanical behavior. These findings provide preliminary mechanical evidence and design insights regarding scaffold performance. However, the results should be interpreted within the scope of mechanical evaluation only and do not provide direct biological validation or evidence of clinical applicability.
Keywords:
biomaterials; bone scaffold; lattice architecture; PLA; stress shielding
1. Introduction
Additive manufacturing (AM) is an emerging production technology that has gained significant traction in recent years due to rapid advancements in digital fabrication. The core principle of AM involves fabricating parts by depositing material layer by layer onto a build platform, a process often referred to as layered manufacturing. Conventional subtractive techniques rely on removing material during production. Additive manufacturing provides greater material efficiency as it deposits material only in the regions required for the final structure. In addition, the method provides a high degree of design freedom and supports the fabrication of geometrically complex structures that traditional manufacturing methods cannot easily achieve. It also enables relatively short production times.
AM has found widespread application across diverse industries such as defense, aerospace, construction, textiles, food production, automotive manufacturing, and, notably, healthcare. In the medical field, additive manufacturing enables the fabrication of patient-specific implants and scaffolds with complex geometries that conventional manufacturing techniques cannot easily produce[1].
Medical applications of AM include 3D bioprinting, personalized implant fabrication, orthopedics, dentistry, and tissue engineering. The ability to manufacture patient-specific medical solutions in a shorter time frame compared to conventional methods has contributed to its widespread integration in modern healthcare.
In clinical settings, implants are commonly used to restore bone tissue that has been damaged or lost due to trauma, disease, or degenerative conditions[2]. Artificial bone scaffolds play a critical role in tissue engineering in cases where natural healing does not provide adequate regeneration. Biodegradable polymeric scaffolds offer a more effective alternative to traditional autograft and allograft approaches, reducing the risk of infection and immune rejection. 3D printing technologies enable the fabrication of patient-specific scaffolds with complex geometries using diverse materials. Laser-based methods provide high precision but face limitations related to cost and cell viability. Non-laser methods provide lower cost, greater material diversity, and higher achievable cell density[3]. The human skeletal system is composed of two main types of osseous tissue: cortical bone and trabecular bone. Cortical bone, which forms the dense outer shell, is characterized by low porosity (5–15%) and small pore sizes, accounting for approximately 80% of the total bone mass in the human body. In contrast, trabecular bone possesses a higher porosity (70–90%) and larger pores, exhibiting a honeycomb-like internal structure and a significantly higher surface-area-to-volume ratio[2,4,5].
Numerous studies have shown that a porosity above 70% enhances osteointegration and facilitates bone regeneration. However, increased porosity also compromises mechanical integrity, making highly porous implants unsuitable for load-bearing regions such as the femur or tibia[5]. Human bone exhibits distinct mechanical and structural characteristics depending on tissue type. Cortical bone generally demonstrates higher stiffness and strength, with compressive strength values ranging from approximately 100–150 MPa and elastic modulus values between 10–20 GPa. In contrast, trabecular bone exhibits considerably lower mechanical properties, with compressive strength values typically ranging from 2–12 MPa and elastic modulus values between 0.1–5 GPa. Structural differences are also evident in porosity characteristics, as cortical bone typically exhibits low porosity values (5–10%), whereas trabecular bone possesses a highly porous architecture with porosity values ranging from 50–90%. These differences play an important role in load transfer behavior and should be considered in the design of mechanically compatible scaffold structures intended to mimic native bone tissue[6-11].
One of the major challenges in orthopedic regenerative medicine is the development of bone scaffolds and implants that closely replicate the biomechanical properties of the host bone[12]. Accordingly, implant design and material selection are critical factors to ensure replacement devices maintain both mechanical integrity and biocompatibility. Implants exhibiting significantly higher stiffness or strength than native bone may impede effective load transfer between the implant and surrounding tissue[13]. As a result, the implant bears a disproportionate share of mechanical stress, and this situation can lead to bone resorption due to reduced mechanical stimulation. This outcome is known as stress-shielding effect[14]. Stress shielding adversely affects osseointegration, ultimately compromising the stability and longevity of the implant[15]. Therefore, meticulous consideration of scaffold design and material properties is essential to minimize the risk of stress shielding and subsequent implant failure, which often necessitates revision surgery[13].
3D printing allows for the fabrication of patient-specific implants that precisely match bone defects. Both biodegradable and non-biodegradable thermoplastics can be used, allowing temporary scaffolds to be gradually replaced by natural bone without surgical removal. Thermoplastics can be enhanced with bioactive additives, such as calcium phosphate ceramics, to improve osteoconductivity and promote better integration with surrounding bone tissue[16]. These challenges have increased the interest in biopolymers, which stand as promising candidates for implant fabrication because they possess favorable mechanical properties and strong biocompatibility.
Within this context, biomaterials and particularly polymer-based materials have gained increasing attention in bone tissue engineering applications[16]. Biomaterials are natural or synthetic materials used in medical devices to replace or restore biological functions within the human body[17]. Biomaterials research has evolved into a multidisciplinary field integrating engineering, chemistry, and life sciences to address complex medical challenges[18]. Among synthetic biomaterials, polymers have gained significant attention due to their biocompatibility, processability, and tailorable mechanical properties[19,20]. In particular, biopolymers such as polylactic acid (PLA) are widely used in biomedical applications because of their biodegradability, low density, and favorable mechanical characteristics. These properties make PLA a suitable candidate for porous bone scaffolds fabricated by additive manufacturing technologies.
The mechanical behavior and biological functionality of porous scaffolds are also strongly influenced by their internal structural architecture. Lattice structures are three-dimensional frameworks composed of the periodic repetition of unit cells, which consist of both solid and void regions. Representative fundamental unit cell geometries commonly used in lattice structures are shown in the Supplementary Material (Figure S1)[21]. Their mechanical behavior is strongly governed by unit cell geometry, relative density, and connectivity between structural elements. Lattice structures incorporate internal voids, making them significantly lighter than solid materials of the same volume. The mechanical performance of lattice structures depends primarily on relative density, unit cell morphology, and deformation mechanisms. Structures with higher connectivity tend to exhibit stretch-dominated mechanical behavior and therefore show greater stiffness. In contrast, bending-dominated architectures usually exhibit lower stiffness but allow higher levels of porosity[22,23]. Lattice structures exhibit high porosity and a large surface-area-to-volume ratio. These properties make them highly suitable for biomedical applications, such as bone scaffolds, which require mechanical compatibility and efficient tissue integration[24].
Although numerous studies have examined lattice structures for orthopedic applications, many existing comparisons rely on different materials, manufacturing techniques, geometric scales, or relative densities. Such variation limits the ability to isolate the influence of lattice topology on mechanical performance. As a result, a systematic evaluation under controlled conditions is necessary to clarify topology-dependent mechanical behavior. It was hypothesized that lattice topology would significantly influence the mechanical response of the investigated structures even under identical material, manufacturing, and geometric conditions.
The present study offers a comparative evaluation of three commonly used lattice architectures, which include Face-Centered Cubic (FCC), Rhombic Faced (RF), and Octet Truss (OT). The structures were manufactured from PLA under identical process parameters and geometric constraints. Mechanical responses were assessed through finite element analysis and quasi-static compression experiments within a porosity range that corresponds to trabecular bone. The use of consistent material properties and manufacturing parameters enables a direct examination of the role of lattice topology in stiffness and its potential contribution to mechanical compatibility in bone scaffold design.
2. Materials and Methods
This study was conducted in three stages. Three lattice architectures, which include Face-Centered Cubic (FCC), Rhombic Faced (RF), and Octet Truss (OT), were selected for systematic comparison under identical material and processing conditions. Design models were created according to the ASTM D1621-16 (2023) standard for test specimens with dimensions of 55.6 × 55.6 × 28.4 mm, and compression analyses were conducted using the finite element method (FEM).
In the second stage, test specimens were fabricated via Fused Deposition Modeling (FDM) using Polylactic Acid (PLA), a biocompatible and biodegradable polymer commonly employed in implant manufacturing.
In the final stage, quasi-static compression tests were carried out to determine the mechanical response of the specimens.
2.1 PLA and its general properties
PLA, or polylactide, is a biodegradable aliphatic polyester widely used in biomedical applications due to its favorable biocompatibility and processability[25,26]. The general physical and mechanical properties of PLA are provided in the Supplementary Material (Table S1).
2.1.1 Determination of properties of PLA material used for experimental specimens
To verify that the PLA material used for the test specimens meets the required mechanical properties and to determine its compressive elastic modulus for finite element analysis, the compression test specimens were designed in accordance with the ASTM D695-23 standard. The specimens, with a diameter of 12.7 mm and a height of 50.8 mm, were modeled using SolidWorks and manufactured via Fused Deposition Modeling (FDM). Compression tests were conducted at a crosshead speed of 1.3 mm/min in accordance with the standard (Figure 1).
(a) Design; (b) Manufactured filled PLA compression specimens; (c) Compression test of filled PLA specimens.
Stress (σ)–strain (%) curves obtained from the compression test data are presented in Figure 2. Based on three tests, the compressive elastic modulus of the fabricated PLA material was determined to be 3092 MPa.
2.2 Lattice structure designs for artificial bone
Three distinct unit cells were initially designed using SolidWorks software, which were subsequently assembled into lattice structures according to the specimen dimensions specified in ASTM D1621-16 (2023) for experimental evaluation. Figure 3 illustrates the unit cell geometry. Each unit cell had an edge length of 8 mm and a strut diameter of 1.2 mm. The lattice structures consisted of arrays of 8 × 8 × 4 unit cells. The final unit cell geometries and corresponding lattice assemblies are illustrated in Figure 4.
Lattice structures used in experimental studies and their corresponding unit cells: (a) FCC unit cell; (b) FCC lattice structure; (c) RF unit cell; (d) RF lattice structure; (e) OT unit cell; (f) OT lattice structure.
The porosity of the designed implant unit cells must be quantified to enable comparison with the porosity of human bone. For this purpose, the following equations were employed:
The values of the unit cells in the equations are: VFV: Filled volume (8x8x8= 512mm3), VPV: Porous volume, VTPD: Total pore density and φ: % Pore density.
The porous volumes (VPV) of the unit cells were calculated using SolidWorks software. The calculations made using Equations 1 and 2 are given in Table 1.
The relative densities (or infill rates) of the lattice structures were calculated using SolidWorks software as 66% for FCC, 41% for RF, and 21% for OT, respectively.
2.3 Finite element analysis of lattice structure designs
Finite element analysis (FEA) was performed on the lattice structures previously modeled in Figure 4. To simulate compression testing conditions, the analysis models incorporated 2-mm-thick plates on the top and bottom surfaces of each lattice structure. Figure S2 in the Supplementary Material illustrates this configuration. These plates were incorporated to ensure uniform load distribution across the entire specimen during loading.
In the FEA simulations, a compressive load was applied via the top plate at a constant rate of 12.5 mm/min, replicating the loading conditions of the physical compression tests (Figure S3).
Finite element simulations were performed in ANSYS 2024R2 using a quadratic tetrahedral mesh under quasi-static nonlinear static structural conditions. Depending on lattice geometry, mesh element sizes ranging from 0.5 to 0.75 mm were employed to adequately represent the global deformation behavior while maintaining computational feasibility. PLA behavior was modeled as isotropic elastic–plastic using literature-based PLA material properties together with a bilinear isotropic hardening model. Bonded contact was defined between the lattice structures and the loading plates to ensure numerical stability and to focus on the global deformation response. Elastic modulus values were determined from the slope of the initial linear region of the simulated stress–strain curves.
2.4 Fabrication of artificial bone test specimens
Test specimens were fabricated using the Fused Deposition Modeling (FDM) technique. In FDM, parts are produced by extruding thermoplastic filaments through a heated nozzle[27]. This method is widely used due to its material availability, low cost, and ease of processing[28]. In the FDM process, molten filament is deposited layer-by-layer following the toolpath generated by the slicing software until the part is completed[29].
The schematic of the FDM process for lattice fabrication is provided in the Supplementary Material (Figure S4).
The test specimens were fabricated using a commercial ELAS PLA Premium filament (1.75 mm diameter, ±0.03 mm dimensional tolerance, density: 1.24 g/cm3) with a 0.4 mm nozzle diameter, a layer thickness of 0.2 mm, a printing speed of 50 mm/s, a printing temperature of 220 °C, a bed temperature of 45 °C, and a Z-axis build orientation (Figure 5). The slicing parameters were defined using 100% infill settings to preserve the designed lattice geometry.
2.5 Compression test of artificial bone test specimens
Compression tests were performed in compliance with the ASTM D1621-16 (2023) standard using a Shimadzu AGS-X 50 kN testing machine, with five specimens prepared for each lattice structure type. A photograph of the experimental compression test setup is provided in the Supplementary Material (Figure S5). The stress (σ, in N/mm2)–strain (%) curves obtained from the compression tests are presented in Figure 6.
Stress (σ)–Strain (%) curves of experimental specimens: (a) FCC specimens and mean curve; (b) RF specimens and mean curve; (c) OT specimens and mean curve; (d) comparison of mean curves for FCC, RF, and OT structures.
3. Results and Discussions
In the lattice structures investigated in the study, the unit cell % pore densities were found to be 55.72% for FCC, 72.62% for RF, and 85.68% for OT, respectively (Table 1). The results indicated that these values fell within the pore density range reported for human trabecular bone tissue.
According to the results of the finite element analyses, the stress (σ)–strain (%) curves for the three lattice structures are presented in Figure 7.
Stress (σ) – Strain (%) curves for the mean values of FCC, RF, and OT units based on finite element analysis.
Based on the finite element analysis data, mean stress-strain curves were generated (Figure 7), and the compressive elasticity modulus values of the lattice structures were determined as 358.16 MPa for FCC, 168.63 MPa for RF, and 145.92 MPa for OT.
The relationship between relative density and elastic modulus in lattice structures can be described through the Gibson–Ashby model for cellular solids[22–24]. According to the model, the elastic modulus of a porous structure scales with relative density according to the following expression:
where (E) is the elastic modulus of the lattice structure, (Es) is the modulus of the solid material, and (ρ / ρs) represents the relative density. The model parameters were obtained by logarithmic transformation of the Gibson–Ashby equation followed by linear regression analysis of the experimental data presented in Figure 8.
Relationship between relative density (ρ/ρs) and compressive elastic modulus of the investigated lattice structures (FCC, RF, and OT) based on experimental compression test results.
Mean stress–strain (%) curves were plotted on the basis of the compression test data (Figure 6d). Calculations derived from these graphs indicated compressive elasticity modulus values of 192.186 MPa for the FCC structure, 97.418 MPa for the RF structure, and 62.162 MPa for the OT structure (Table 2).
Experimental elastic modulus values and statistical parameters of the investigated lattice structures.
To statistically evaluate the differences in elastic modulus among the investigated lattice structures, a one-way analysis of variance (ANOVA) was performed based on the experimental compression test results. The analysis indicated that lattice topology has a statistically significant effect on the compressive elastic modulus (F = 3293.868, p < 0.0001), confirming a clear stiffness hierarchy among the investigated lattice topologies (Table 3).
The results demonstrate that the differences in elastic modulus among the FCC, RF, and OT lattice structures are statistically significant.
The relationship between relative density and elastic modulus derived from the experimental results is illustrated in Figure 8.
A logarithmic fitting procedure based on the Gibson–Ashby model yielded an exponent value of n = 0.983 and a coefficient C = 0.128 with a goodness-of-fit of R2 = 0.960. The fitted relationship showed agreement with the experimental trend, indicating consistency between the observed mechanical response and established cellular solid theory. However, the limited number of experimental data points should be considered when interpreting the model parameters and the predictive capability of the fitted relationship. The fitting should be interpreted cautiously due to the limited number of experimental data points.
The results reveal several observations regarding the influence of lattice topology on mechanical performance and scaffold characteristics. All three lattice architectures exhibit pore density values within the range commonly reported for trabecular bone tissue. This observation indicates structural similarities in terms of porosity characteristics. Such correspondence alone cannot be considered sufficient to infer biological performance or biomedical applicability. However, despite comparable biological relevance in terms of porosity, the mechanical responses differ significantly according to lattice topology. This observation demonstrates that pore density alone cannot predict structural performance. The geometry and connectivity of the struts play a dominant role in the determination of structural stiffness.
Pore density values within this range have been reported in the literature to be associated with structural characteristics considered relevant for porous scaffold design. Such features may contribute to favorable conditions for tissue-related functionality. Nevertheless, the present study evaluates only mechanical behavior and does not provide direct biological validation. Since FCC, RF, and OT all satisfy this pore density range, comparisons in the present work should be interpreted primarily from a mechanical and structural perspective.
From a mechanical perspective, the experimental results demonstrate a clear topology-dependent hierarchy in mechanical performance, with FCC exhibiting the highest stiffness, followed by RF and OT. This trend is consistent with the relative density differences among the structures and with established theories for cellular solids, which indicate that the relationship between elastic modulus and relative density depends strongly on deformation mechanisms and structural architecture. This behavior is also consistent with recent findings reported in the literature, where lattice topology and deformation mechanisms were identified as key parameters governing stiffness and mechanical response. Stretch-dominated architectures generally exhibit superior load-bearing capability and stiffness compared to bending-dominated structures due to more efficient force transmission pathways[30]. The higher stiffness of the FCC architecture can be attributed to its more efficient load-bearing pathways and greater strut connectivity, which promote axial load transfer rather than bending-dominated deformation.
These observations are also consistent with previous studies on FDM/FFF-fabricated lattice structures. Liu et al. reported that increasing relative density resulted in a substantial increase in elastic modulus, while manufacturing-induced defects contributed to deviations between experimental and numerical predictions[31]. Similarly, Bagheri et al. demonstrated that octet-truss structures with higher relative densities exhibited significantly greater elastic modulus values, further supporting the strong influence of geometry and structural architecture on mechanical performance[32].
However, the arrangement and geometry of the pores have a greater influence than the pore density alone. For instance, the regular and symmetrical pore distribution in the FCC structure may provide advantages in load transfer and mechanical stability, whereas the RF and OT designs, despite offering higher pore densities, may be more limited in terms of mechanical strength.
The discrepancy between finite element predictions and experimental measurements can be attributed to manufacturing-induced defects inherent to the FDM process, such as imperfect interlayer bonding, dimensional deviations, and surface roughness. These factors reduce the effective load-bearing cross-section and introduce stress concentrations, leading to lower measured stiffness compared to idealized numerical models. Similar observations have been reported in recent studies, where process-induced defects and geometric irregularities in additively manufactured lattice structures resulted in stress heterogeneity and deviations between experimental and numerical mechanical responses[31]. Therefore, in practical applications, the choice of design should be based not only on pore density but also on the expected mechanical performance and specific functional and mechanical requirements.
From a design perspective, the results indicate that FCC-type lattices may provide advantageous mechanical characteristics for applications requiring higher stiffness. In contrast, RF and OT architectures may be considered suitable alternatives for applications that prioritize high porosity and reduced mass, based solely on their mechanical characteristics. Consequently, the selection of lattice topology should depend on the targeted balance between mechanical support and biological functionality rather than on porosity alone.
4. Conclusions
This study presents a systematic mechanical comparison of three widely used lattice architectures, namely Face-Centered Cubic (FCC), Rhombic Faced (RF), and Octet Truss (OT), which were manufactured from PLA under identical process conditions. The results demonstrate that lattice topology exerts a pronounced influence on the compressive behavior of porous structures, even when material properties, manufacturing parameters, and geometric scale remain constant. The pore density values of the investigated FCC, RF, and OT lattice structures were found to fall within ranges commonly reported for trabecular bone tissue, indicating structural similarities in terms of porosity characteristics.
Among the investigated designs, the FCC architecture exhibited the highest stiffness, followed by RF and OT, indicating a clear topology-dependent hierarchy in load-bearing capacity. This finding highlights the importance of structural connectivity and load transfer mechanisms in determining the mechanical performance of lattice scaffolds.
Discrepancies between experimental compression tests and finite element predictions are consistent with common additive manufacturing defects, including incomplete interlayer fusion, micropores at lattice junctions, and surface roughness in the absence of post-processing. Such manufacturing-induced imperfections adversely affect the compressive behavior of fabricated specimens and have been reported previously[32]. Therefore, these factors should be considered when interpreting the mechanical response of FDM-fabricated lattice structures and when comparing experimental results with idealized numerical models.
Future studies may investigate geometric modifications, such as increased strut thickness, to evaluate their influence on the mechanical response of RF and OT lattice structures. Similarly, future studies may investigate geometric optimization strategies for all three architectures to further examine topology–property relationships.
Overall, the results provide practical guidance for selecting lattice architectures according to desired mechanical performance, emphasizing that lattice topology plays an important role in the design of porous load-bearing structures. Future work should incorporate biological, degradation, fatigue, and long-term performance evaluations to further assess the broader applicability of these structures.
Supplementary Material
Supplementary material accompanies this paper.
Figure S1
Table S1
Figure S2
Figure S3
Figure S4
Figure S5
This material is available as part of the online article from https://doi.org/10.1590/0104-1428.20260019
5. Acknowledgements
This research was supported by The Scientific Research Projects Coordination Unit of Sivas Cumhuriyet University (Project No: TEKNO-2024-041). The study did not involve any human participants or animals; therefore, ethical approval was not required. The data that support the findings of this study are available from the corresponding author upon reasonable request. The manuscript was prepared by a single author, and there are no conflicts of interest to declare.
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