Effect of framework material and gyroid lattice design on the biomechanics of all-on-four full-arch prostheses

Abstract

Background

This finite element analysis (FEA) aimed to evaluate the biomechanical behavior of all-on-four implant-supported full-arch prostheses fabricated from different framework materials and internal designs.

Methods

Three-dimensional FEA models were constructed to simulate bar- and Toronto-type frameworks made of cobalt–chromium (Co–Cr), titanium (Ti), and polyetheretherketone (PEEK) materials. Each framework was modeled as a conventional solid structure, and metallic frameworks were also modeled with a gyroid lattice design. Vertical and oblique (30°, 150 N) loading conditions were applied to replicate masticatory forces. von Mises and principal stresses were analyzed for the framework, implant, abutment, and surrounding bone.

Results

Gyroid lattice frameworks exhibited 10–25% lower internal framework stresses but transmitted 12–22% higher stresses to the implant body, abutment, and abutment screw compared with solid designs. Cortical and trabecular bone stresses remained within physiological limits. PEEK frameworks demonstrated the lowest internal stresses yet exhibited the highest deformation due to their lower elastic modulus. Metallic frameworks, particularly Ti, showed higher rigidity and more balanced stress transfer. Toronto-type designs displayed more homogeneous stress distribution and lower peak stress values than bar-type frameworks. Under vertical loading, the smallest framework–bone deformation difference was observed in the Toronto-gyroid Co–Cr framework (2.73 μm), and the highest in the bar-gyroid PEEK framework (12.63 μm). Under oblique loading, the Toronto-gyroid Co–Cr model again exhibited the lowest deformation difference (6.67 μm), while the bar-gyroid PEEK framework showed the highest (16.87 μm).

Conclusions

The Toronto-gyroid Co–Cr and Ti frameworks showed a more balanced load distribution and smaller framework–bone deformation differences under the tested conditions, whereas the PEEK frameworks demonstrated greater flexibility.

Background

Dental implants have become a standard treatment modality in modern dental practice, with their consistently high survival rates making them the preferred choice for prosthetic rehabilitation in many situations [1].The all-on-four concept is based on the placement of two anterior axially positioned implants and two posterior implants tilted distally to reduce cantilever length and optimize load distribution. In this configuration, the two anterior implants are positioned axially, whereas the posterior implants are inclined distally to minimize cantilever length and facilitate the fabrication of prostheses comprising up to twelve teeth, thereby optimizing the masticatory performance of the restoration [2].

In the context of implant-supported full-arch prostheses, incorporating a rigid framework is indispensable for securing the artificial dentition [3]. Implant-supported bars may be compared to structural beams in engineering, as both function as fundamental load-bearing elements. The ability to withstand bending stresses and provide adequate strength and rigidity is essential for maintaining structural integrity and ensuring efficient load transfer.

Metallic alloys remain the preferred materials for such frameworks, primarily due to their superior tensile strength (> 300 MPa) and elastic modulus (> 80,000 MPa), which effectively mitigate the risk of plastic deformation in cantilever segments [4]. Among these Co-Cr alloy has gained widespread clinical application [5].

Titanium (Ti) alloys have subsequently emerged as a promising alternative for CAD/CAM-based fabrication of implant frameworks, demonstrating excellent long-term success rates (92.4–100%) and superior biocompatibility [6]. Their chemical stability effectively eliminates the risk of galvanic corrosion, a limitation often observed in conventional non-noble metal alloys, while their rigidity and flexural resistance further enhance the mechanical durability of the framework [7].

Polyetheretherketone (PEEK), a high-performance thermoplastic polymer within the polyaryletherketone (PAEK) family, has attracted increasing scientific and clinical interest as an alternative framework material [8] PEEK exhibits excellent biocompatibility and an elastic modulus closely resembling that of cortical bone and dentin [9].

Recent advances in design optimization have introduced lattice-structured frameworks, which can effectively reduce stress transmission under impact loading and mitigate local buckling of surface layers [10]. These internal architectures preserve mechanical integrity while significantly reducing material use and overall weight [11]. Belonging to the Triply Periodic Minimal Surface (TPMS) family, such lattice structures feature continuously interconnected geometries. Among them, the gyroid lattice has gained particular attention as one of the most distinctive and widely investigated configurations due to its uniform stress distribution and superior mechanical efficiency [12, 13]. Its mathematically definable and highly adaptable geometry also enables precise structural modulation, facilitating customization for specific biomedical applications [14].

Biomechanical considerations are critical in the long-term success of implant-supported restorations. Excessive functional loading can induce stress and deformation in the surrounding bone; while physiological stress supports normal remodeling, exceeding the elastic threshold may lead to microdamage or bone resorption [15]. Factors such as load magnitude and direction, prosthesis design, implant configuration, and bone quality significantly influence clinical outcomes .16]. Notably, higher failure rates have been reported in the posterior maxilla than in the mandible, emphasizing the importance of implant positioning and biomechanical control in the maxillary region [17]. Several analytical methods such as strain gauge analysis, photoelastic techniques, and FEA have been employed to evaluate stress distribution in implant systems. Among these, FEA is the most widely used, providing a non-destructive computational approach to simulate and assess mechanical behavior under various loading conditions [18]. By discretizing complex structures into smaller elements, FEA enables precise investigation of material behavior and comparison of design configurations [19].

Little evidence exists regarding how internal lattice architectures influence load transmission in full-arch prosthetic systems designed with the all-on-four configuration. Therefore, the aim of this study was to assess and compare the biomechanical behavior of different framework materials, Co–Cr alloy, Ti alloy, and PEEK, incorporating an internal gyroid lattice design in all-on-four implant-supported full-arch prostheses using FEA. This study is novel in that it integrates a gyroid lattice design into a full-arch all-on-four prosthetic system and compares its biomechanical performance across different framework materials and prosthetic configurations under identical modeling conditions. In addition to stress analysis, differences in framework–bone displacement were also evaluated to provide further insight into load transfer behavior. The null hypothesis of this study was that the framework material (Co–Cr, Ti, or PEEK) and internal design (solid or gyroid) would not significantly affect the stress distribution or deformation patterns within the framework, implant components, or surrounding bone in implant-supported full-arch prostheses.

Materials and methods

Three-dimensional (3D) finite element models were constructed to evaluate the biomechanical behavior of different framework materials and internal designs in all-on-four implant-supported prostheses. All modeling and analysis were performed on HP workstations equipped with an Intel Xeon E-2286 processor (2.40 GHz) and 64 GB of ECC memory.

The bone model was reconstructed from computed tomography data of the Visible Human Project (National Library of Medicine, Maryland, USA) [20]. Tomographic slices with a thickness of 0.33 mm were imported into 3D Slicer (v5.2.2, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA) in DICOM format, segmented according to Hounsfield unit thresholds (426.50–3193.04), and exported in STL format after removal of unwanted regions and artifacts. The STL files were then processed in Blender (version 3.6, Blender Foundation, Amsterdam, Netherlands) for reverse engineering and geometric refinement. A cortical bone layer with a thickness of 2 mm was generated by applying an inward offset to the external bone surface, and the inner trabecular structure was modeled using the inner contour of the cortical layer. All anatomical components were properly aligned in a 3D coordinate system to ensure geometric accuracy.

3D CAD models of dental implants (Nobel Parallel CC, 4.3 mm diameter, 10 mm anterior and 13 mm posterior lengths; Nobel Biocare AB, Göteborg, Sweden) and corresponding multi-unit abutments (0° straight and 30° angulated) were generated according to the manufacturer’s specifications. Implants were positioned at the sites corresponding to teeth #2 and #5. Straight abutments with 2.5 mm gingival height were assigned to the anterior implants, and 30° angulated abutments with 3.5 mm gingival height were used posteriorly, following the Nobel Biocare catalog dimensions.

Two prosthetic configurations were designed: a Bar system and a Toronto system. Each configuration was initially modeled as a solid structure and subsequently modified to include a gyroid lattice with an internal geometry of 0.8 mm, corresponding to the lattice wall thickness. For the Toronto framework, monolithic zirconia crowns were modeled for the teeth, and a 1-mm feldspathic porcelain layer was applied to represent the gingival portion. A 0.1 mm cement layer was positioned between the Toronto framework and the suprastructure. In contrast, for the bar-type prosthetic design, acrylic resin teeth were modeled as the superstructure material in accordance with conventional clinical hybrid prosthesis protocols. All prosthetic assemblies incorporated a 10-mm cantilever extension. The alignment and mesh compatibility among all components were verified using Altair HyperMesh (version 2023.1, Altair Engineering Inc., Troy, MI, USA) (Fig. 1).

Fig. 1.

Finite element models of the four framework configurations: (A) Bar–Solid, (B) Bar–Gyroid, (C) Toronto–Solid, and (D) Toronto–Gyroid. Bone transparency was increased to visualize implant positioning. The upper panels illustrate the implant–bone relationship and abutment orientation, clearly demonstrating the posterior tilted implants according to the All-on-Four configuration

Four main framework designs were generated: M1 – Bar Solid, M2 – Bar Gyroid, M3 – Toronto Solid, and M4 – Toronto Gyroid. Each main model was subdivided by framework material, yielding 10 submodels (M1-1 to M4-2). Solid frameworks were constructed from Co–Cr alloy, Ti alloy, and PEEK, whereas gyroid frameworks were modeled using Co-Cr and Ti alloys (Table 1).

Table 1.

Model coding, material grouping, and mesh details

Main Model	Model Code(s)	Material Variations	Framework Type	Total Nodes	Total Elements
M1	M1-1	Co–Cr	Bar system with solid frameworks	625,394	2,481,464
	M1-2	Ti
	M1-3	PEEK
M2	M2-1	Co–Cr	Bar system with gyroid lattice frameworks	606,171	2,383,052
	M2-2	Ti
M3	M3-1	Co–Cr	Toronto system with solid frameworks	764,924	2,882,081
	M3-2	Ti
	M3-3	PEEK
M4	M4-1	Co–Cr	Toronto system with gyroid lattice frameworks	694,688	2,628,845
	M4-2	Ti

All materials were assumed to be isotropic, homogeneous, and linearly elastic. For the gyroid frameworks, the effective elastic modulus (E) was recalculated according to the Gibson–Ashby model for cellular solids, which predicts the mechanical properties of porous materials based on the solid material properties and porosity (φ). The relationship is expressed as:

where is the elastic modulus of the solid material and represents the porosity ratio. In this study, the porosity of the gyroid lattice structure was approximately 60%. The selected porosity (60%) falls within the commonly reported range (50–90%) for porous implant structures, which has been shown to provide a balance between mechanical stability and stress reduction. Therefore, this value was selected as a representative parameter within the reported biomechanical range rather than an optimized or exclusive value [21, 22]. Using this relation, the effective elastic modulus values were calculated as 8.72 GPa for Co–Cr alloy (solid GPa) and 4.40 GPa for Ti alloy (solid GPa). These values were subsequently assigned to the gyroid framework models to represent their realistic mechanical behavior. This calculation approach was based on the Gibson–Ashby relationship, which describes the dependence of elastic modulus on relative density in cellular solids [23]. In this study, the gyroid lattice structures were represented using a homogenized material approach based on an effective elastic modulus derived from the Gibson–Ashby model, rather than explicitly modeling the detailed porous geometry. It should be noted that this homogenized modeling approach represents a macro-scale approximation and may underestimate localized micro-stresses within the lattice struts.

The mechanical properties assigned to each material are summarized in Table 2 [23–26].

Table 2.

Material properties used in the finite element analysis

Material	Elastic Modulus (MPa)	Poisson’s Ratio
Cortical bone	13,700	0.30
Trabecular bone	1,370	0.30
Co-Cr alloy (Solid)	218,000	0.33
Co-Cr alloy (Gyroid lattice)	34,880	0.33
Titanium (Solid)	110,000	0.35
Titanium (Gyroid lattice)	17,600	0.35
PEEK	4,100	0.40
Zirconia	210,000	0.30
Acrylic resin	3,000	0.30
Feldspathic porcelain	82,800	0.35
Cement	11,860	0.30

Surface meshing was performed using refined triangular (tria) elements with sizes ranging from 0.10 to 0.25 mm, followed by solid meshing using tetrahedral elements. Mesh convergence was evaluated based on the variation in the maximum von Mises stress in critical regions (implant neck and cortical bone) with a threshold of less than 3% considered acceptable (Fig. 2). The total number of nodes and elements for the four primary models is listed in Table 1. Boundary conditions were defined by constraining all degrees of freedom at the superior regions of the cortical and trabecular bone to prevent displacement. Contact interfaces between all components were defined as bonded (tie) contact conditions, ensuring complete displacement compatibility and preventing relative motion between surfaces. Accordingly, the implant–bone interface was modeled as fully bonded, assuming complete osseointegration, as is commonly adopted in finite-element analyses of implants [27].

Fig. 2.

Representative finite element mesh images showing (A) mesh refinement within the gyroid framework region and (B) detailed mesh at the implant–abutment interface, demonstrating local mesh densification in critical stress concentration areas

Two loading conditions were simulated under linear static analysis using Altair OptiStruct Solver (version 2023.1, Altair Engineering Inc., Troy, MI, USA). In the first scenario, a unilateral vertical load of 150 N was applied. The load was distributed as 50 N on the palatal cusp of tooth #25 and 100 N on the palatal cusps of tooth #26 [28, 29]. In the second scenario, a unilateral oblique load of 150 N was applied to the same region at an angle of 30° to the long axis, directed from the palatal toward the buccal side. To prevent stress singularities, the loads were evenly distributed among adjacent nodes (Fig. 3).

Fig. 3.

Loading conditions applied in the finite element analysis: (A) unilateral vertical load (150 N) applied to the posterior region, and (B) unilateral oblique load (150 N) applied at 30° to the long axis of the implants

For each condition, total displacement values (µm) of both framework(FW) and bone were obtained to assess deformation behavior. The difference between framework and bone displacement (ΔFW–Bone) and FW/Bone ratio were calculated to quantify structural flexibility and load transfer efficiency within each model.

Each of the 10 models was analyzed under both vertical and oblique loading conditions, resulting in a total of 20 finite element analyses. von Mises stresses were calculated to evaluate the stress distribution within the implants and abutments, while maximum and minimum principal stresses were used to assess stress patterns in bone tissue. All results were visualized using consistent color scales within each figure set to enable reliable comparison of stress magnitudes among different framework designs and materials under identical loading conditions.

Results

Finite element analysis revealed distinct variations in stress distribution and deformation patterns depending on the framework material, internal structure, and loading condition. Both vertical and oblique loading scenarios demonstrated consistent stress trends across all models (M1–M4).

The maximum von Mises stress values for the implants and their components are presented in Table 3. Under vertical loading, the highest von Mises stress within the frameworks was observed in the bar-type system (M1), particularly in the solid Co–Cr configuration (M1-1, 90.201 MPa). The lowest stress occurred in the Toronto gyroid Ti system (M4-2, 26.512 MPa) (Fig. 4).

Table 3.

Maximum von Mises stress values (MPa) under vertical and oblique loading conditions

Model	Vertical loading				Oblique loading
	Framework	Implant	Abutment	Abutment screw	Framework	Implant	Abutment	Abutment screw
M1-1	90.201	79.417	89.072	69.354	111.518	165.878	191.336	87.762
M1-2	83.380	88.077	101.989	93.759	108.862	213.294	249.109	158.146
M1-3	79.587	86.441	114.196	167.053	96.595	229.752	276.545	486.228
M2-1	70.631	92.215	105.583	55.563	99.011	259.253	311.056	86.944
M2-2	67.361	96.892	116.848	74.425	82.237	240.596	289.732	153.640
M3-1	38.713	56.922	57.052	19.380	90.413	85.545	94.522	28.357
M3-2	36.584	62.001	63.827	25.869	88.589	114.058	128.797	37.813
M3-3	34.003	73.924	105.945	77.146	62.649	165.188	194.267	186.219
M4-1	28.836	74.646	75.044	18.360	68.229	171.732	200.830	27.805
M4-2	26.512	74.894	95.944	22.631	62.581	166.556	195.281	36.079

Fig. 4.

von Mises stress distribution in the framework structures under vertical loading conditions. Models are arranged from left to right within each row as follows: Row 1: M1-1, M1-2, M1-3; Row 2: M2-1, M2-2; Row 3: M3-1, M3-2, M3-3; Row 4: M4-1, M4-2. The color scale represents stress magnitude (MPa).The internal gyroid lattice structure is represented through homogenized material properties and is not visually distinguishable in the stress contour plots

When oblique loading was applied, all groups exhibited increased stress magnitudes. The highest framework stress (111.518 MPa) was found in M1-1, followed by M1-2 (108.862 MPa), whereas the lowest stress was observed in M4-2 (62.581 MPa) (Fig. 5).

Fig. 5.

von Mises stress distribution in the framework structures under oblique loading conditions. Models are arranged from left to right within each row as follows: Row 1: M1-1, M1-2, M1-3; Row 2: M2-1, M2-2; Row 3: M3-1, M3-2, M3-3; Row 4: M4-1, M4-2. The color scale represents stress magnitude (MPa).The internal gyroid lattice structure is represented through homogenized material properties and is not visually distinguishable in the stress contour plots

Implant stresses followed a similar pattern. Under vertical loading, the lowest von Mises stress was 56.922 MPa (M3-1) (Fig. 6), whereas under oblique loading, the highest stress value reached 259.253 MPa (M2-1) (Fig. 7). In all models, the highest stress values were consistently observed in the posterior implants on the loading side. Stress concentrations were primarily localized at the implant neck in the cortical crest region, followed by the abutment platform–implant interface. For the abutment screws, peak stresses were mainly detected at the screw head and the first thread adjacent to the implant–abutment connection. Under vertical loading, the lowest abutment stress was observed in M3-1 (57.052 MPa) (Fig. 8), whereas under oblique loading, the highest stress occurred in M2-1 (311.056 MPa) (Fig. 9). For abutment screws, the highest von Mises stress was 486.228 MPa (M1-3) under oblique loading, while the lowest value was 18.360 MPa (M4-1) under vertical loading (Table 3; Figs. 10 and 11).

Fig. 6.

von Mises stress distribution in the implants under vertical loading conditions. Models are arranged from left to right within each row as follows: Row 1: M1-1, M1-2, M1-3; Row 2: M2-1, M2-2; Row 3: M3-1, M3-2, M3-3; Row 4: M4-1, M4-2. The color scale represents stress magnitude (MPa)

Fig. 7.

von Mises stress distribution in the implants under oblique loading conditions. Models are arranged from left to right within each row as follows: Row 1: M1-1, M1-2, M1-3; Row 2: M2-1, M2-2; Row 3: M3-1, M3-2, M3-3; Row 4: M4-1, M4-2. The color scale represents stress magnitude (MPa)

Fig. 8.

von Mises stress distribution in the abutments under vertical loading conditions. Models are arranged from left to right within each row as follows: Row 1: M1-1, M1-2, M1-3, M2-1, M2-2; Row 2: M3-1, M3-2, M3-3, M4-1, M4-2. The color scale represents stress magnitude (MPa)

Fig. 9.

von Mises stress distribution in the abutments under oblique loading conditions. Models are arranged from left to right within each row as follows: Row 1: M1-1, M1-2, M1-3, M2-1, M2-2; Row 2: M3-1, M3-2, M3-3, M4-1, M4-2. The color scale represents stress magnitude (MPa)

Fig. 10.

von Mises stress distribution in the abutment screws under vertical loading conditions. Models are arranged from left to right within each row as follows: Row 1: M1-1, M1-2, M1-3, M2-1, M2-2; Row 2: M3-1, M3-2, M3-3, M4-1, M4-2. The color scale represents stress magnitude (MPa)

Fig. 11.

von Mises stress distribution in the abutment screws under oblique loading conditions. Models are arranged from left to right within each row as follows: Row 1: M1-1, M1-2, M1-3, M2-1, M2-2; Row 2: M3-1, M3-2, M3-3, M4-1, M4-2. The color scale represents stress magnitude (MPa)

A comparative analysis of the internal framework architectures revealed that framework stiffness directly affected stress distribution.

Solid frameworks, characterized by a higher elastic modulus and density, absorbed most of the applied load within the framework itself, resulting in higher von Mises stress concentrations.

In contrast, gyroid frameworks, composed of a 0.8 mm lattice structure, exhibited markedly lower stiffness. This reduction in rigidity decreased the stress levels within the framework but increased the stress transmitted to the implant–abutment complex and bone tissue.

Framework stresses were lower in gyroid models compared with solid models, as indicated by the numerical data in Table 3, where the reduction ranged from approximately 10% to 25%, depending on the material and loading condition.

For example, implant stress increased from 79.417 MPa (M1-1) to 92.215 MPa (M2-1), and abutment stress increased from 89.072 MPa to 105.583 MPa.

The maximum and minimum principal stress values for cortical and trabecular bone under vertical and oblique loading conditions are summarized in Table 4, while the distribution of maximum principal stress in the cortical bone is illustrated in Figs. 12 and 13. Principal stress analysis showed that cortical bone consistently experienced higher stress magnitudes than trabecular bone.

Table 4.

Maximum and minimum principal stress (MPa) in bone under loading conditions

	Vertical loading				Oblique loading
	Max principal		Min principal		Max principal		Min principal
	Cortical bone	Trabecular bone	Cortical bone	Trabecular bone	Cortical bone	Trabecular bone	Cortical bone	Trabecular bone
M1-1	8.746	1.323	-31.471	-2.145	19.076	2.758	-48.035	-2.838
M1-2	9.321	1.472	-34.056	-2.242	24.983	3.522	-57.027	-3.586
M1-3	11.301	1.325	-34.497	-2.359	28.372	3.743	-63.910	-3.962
M2-1	11.354	1.248	-33.970	-2.361	26.899	3.819	-62.555	-3.926
M2-2	11.592	1.375	-34.813	-2.345	29.618	3.932	-65.001	-4.084
M3-1	7.144	1.302	-25.512	-1.890	10.859	1.452	-34.433	-2.616
M3-2	7.471	1.307	-27.129	-1.961	13.726	1.916	-40.331	-2.624
M3-3	8.795	1.354	-30.683	-2.192	20.284	2.752	-52.107	-3.059
M4-1	8.800	1.324	-30.895	-2.187	19.803	2.626	-49.554	-2.803
M4-2	8.970	1.353	-30.921	-2.213	20.649	2.826	-52.464	-2.975

Fig. 12.

Maximum principal stress distribution in the cortical bone under vertical loading conditions. Models are arranged from left to right within each row as follows: Row 1: M1-1, M1-2, M1-3; Row 2: M2-1, M2-2; Row 3: M3-1, M3-2, M3-3; Row 4: M4-1, M4-2. The color scale represents stress magnitude (MPa)

Fig. 13.

Maximum principal stress distribution in the cortical bone under oblique loading conditions. Models are arranged from left to right within each row as follows: Row 1: M1-1, M1-2, M1-3; Row 2: M2-1, M2-2; Row 3: M3-1, M3-2, M3-3; Row 4: M4-1, M4-2. The color scale represents stress magnitude (MPa)

Under vertical loading, the maximum principal stress in cortical bone ranged from 7.144 MPa (M3-1) to 11.592 MPa (M2-2), while in trabecular bone, it ranged from 1.248 MPa (M2-1) to 1.472 MPa (M1-2).

The corresponding minimum (compressive) stresses in cortical bone varied between − 25.512 MPa (M3-1) and − 34.813 MPa (M2-2), whereas in trabecular bone they ranged from − 1.890 MPa (M3-1) to − 2.361 MPa (M2-1).

Under oblique loading, both tensile and compressive stresses increased notably.

The highest maximum principal stress in cortical bone was 29.618 MPa (M2-2), and the highest compressive stress reached − 65.001 MPa (M2-2).

Trabecular bone exhibited lower overall stress values, ranging from 3.932 MPa (M2-2) to − 4.084 MPa (M2-2).

Under both loading conditions, framework deformation was consistently higher than bone deformation. Under vertical loading, framework displacement ranged from 3 to 13 μm, while bone displacement remained below 1 μm (Table 5). Under oblique loading, both values increased, with framework displacement reaching up to 19 μm (PEEK). The gyroid frameworks of Co–Cr and Ti exhibited slightly higher deformation magnitudes than their solid counterparts under both loading conditions. In contrast, the PEEK frameworks demonstrated markedly higher deflection values (Table 6).

Table 5.

Displacement comparison under vertical loading

Model	Bone (µm)	Framework (µm)	Δ (FW–Bone) (µm)	FW/Bone Ratio
M1-1	0.4335	6.452	6.019	14.88
M1-2	0.4258	7.710	7.284	18.11
M1-3	0.4471	13.08	12.63	29.26
M2-1	0.4273	6.916	6.489	16.18
M2-2	0.4254	8.181	7.756	19.23
M3-1	0.5158	3.252	2.736	6.31
M3-2	0.4750	3.653	3.178	7.69
M3-3	0.4036	5.724	5.320	14.18
M4-1	0.4958	3.515	3.019	7.09
M4-2	0.4596	3.978	3.518	8.66

FW framework, Δ = difference between framework and bone displacement, µm micrometer

Table 6.

Displacement comparison under oblique loading

Model	Bone (µm)	Framework (µm)	Δ(FW–Bone) (µm)	FW/Bone Ratio
M1-1	1.980	13.16	11.18	6.65
M1-2	1.995	15.00	13.01	7.52
M1-3	1.980	18.85	16.87	9.52
M2-1	1.972	13.81	11.84	7.00
M2-2	1.960	15.41	13.45	7.86
M3-1	1.752	8.424	6.672	4.81
M3-2	1.781	9.239	7.458	5.19
M3-3	1.900	15.47	13.57	8.15
M4-1	1.748	8.924	7.176	5.10
M4-2	1.769	9.996	8.227	5.65

FW framework, Δ = difference between framework and bone displacement, µm micrometer

Discussion

The present study evaluated the influence of different framework materials and internal designs on the biomechanical behavior of implant-supported full-arch prostheses.

The results demonstrated notable variations in stress magnitudes and distribution patterns depending on the framework type, material, and loading direction.

Therefore, the null hypothesis of this study, which stated that the framework material and internal design would not significantly affect stress distribution or deformation patterns, was rejected.

The finite element model in this study was designed to simulate the all-on-four treatment concept, a widely accepted approach for restoring edentulous arches using four strategically angled implants. This configuration minimizes the need for grafting while providing favorable load distribution along the arch [30, 31. Numerous biomechanical and clinical studies have extensively investigated the all-on-four concept, demonstrating its effectiveness in load distribution, implant stability, and long-term clinical performance [2, 32–34].

The use of full-arch bar systems in implant-supported prostheses aims to enhance rigidity and distribute occlusal loads evenly across multiple implants. However, variations in bar geometry, cross-section, and internal structure can significantly affect the way stresses are transferred through the framework and implants. In this study, two different bar designs were compared to determine the influence of internal architecture on biomechanical performance.

FEA has been widely utilized in previous implant biomechanics studies to predict stress distribution under clinical loading conditions. The model was validated through comparison with previously published numerical and experimental studies, demonstrating consistency in stress distribution patterns and magnitude ranges [30, 35, 36]. Although oblique loading is considered to more accurately represent functional occlusal forces, several previous FEA studies have incorporated both vertical and oblique load applications to achieve a more comprehensive simulation of masticatory conditions [16, 28, 37–39]. Similarly, Almeida et al. [38] and Gönül et al. [28] reported that oblique loading produced higher cortical and implant stresses than vertical loading, which supports the current results.

Modifications in bar design, including lattice architectures and variations in cross-sectional geometry, may influence the biomechanical response of implant-supported frameworks [40]. Lattice frameworks, in particular, have been proposed as an alternative design approach to modify stiffness distribution and stress transfer characteristics within implant-supported prostheses [41]. The gyroid structure was selected as a representative TPMS geometry due to its superior load distribution capacity and manufacturability through additive manufacturing. This type of internal design allows weight reduction while maintaining structural continuity [42]. Gyroid frameworks demonstrated lower internal stresses within the framework (62.581–99.011 MPa) compared with solid designs (88.589-111.518 MPa), while slightly increasing the stress values observed at the implant complex interfaces (166.556-289.732 MPa). The maximum stress values observed in cortical and cancellous bone were within the physiological limits reported in the literature, ranging from 45 to 55 MPa for cortical bone and 5–10 MPa for trabecular bone. [23, 43].

The findings are consistent with those of Lemaire et al. [41], who reported that lattice-optimized titanium frameworks maintained peri-implant strains within the physiological range. Although Koçak et al. [11] and Ekren et al. [44] conducted in vitro mechanical tests rather than numerical simulations, their findings parallel the present FEA results, showing that internal hollowing or lattice filling of Co–Cr frameworks reduces weight while maintaining adequate mechanical strength and stiffness. Parallel to these studies, Ren et al. [45] demonstrated that a functionally graded gyroid framework for implant-supported complete dentures reduced the maximum equivalent stress to below 250 MPa under a 480 N loading, while also halving the weight. Similarly, Alemayehu et al. [14] demonstrated that hybrid gyroid implants, which combine a solid cervical region with a lattice body, effectively minimize micromotions under a 118 N oblique dynamic load. The present study parallels these observations by showing that the gyroid configuration reduced internal framework stresses while redistributing load toward the implant–abutment complex under the tested conditions.

The framework material also significantly affected the biomechanical response.PEEK served as a low-modulus reference material, enabling comparison of how elastic modulus influences stress distribution and deformation. The gyroid lattice design was not applied to PEEK, as such structures are more commonly studied in metallic systems and remain limited in PEEK frameworks. Recent studies have focused on conventional metals, such as Ti and Co–Cr, versus polymer-based materials, including PEEK [46–48]. In general, metal frameworks are much stiffer, whereas PEEK is lightweight with an elastic modulus closer to bone [48]. In the present study, all framework materials were analyzed within an identical model geometry to enable a direct and standardized comparison of how differences in elastic modulus influence load transfer and stress distribution in full-arch implant-supported prostheses. The observed stress patterns were consistent with previous FEA studies reporting higher stiffness and stress concentration in metallic frameworks compared with polymer-based materials [46, 49]. These results align with those of Chang et al. [31], who found that PEEK exhibited lower stress but poor stress dissipation, and with Chen et al. [50], who observed increased implant stress in flexible PEEK frameworks under extended spans. Farouk Zaki Mohamed et al. [46] also observed that PEEK bars produced lower internal framework stress (8.3 MPa) but accumulated greater internal load under oblique forces (168 MPa), while titanium showed more balanced stress transfer to bone. Clinically, the increased stress observed in abutment screws in low-modulus frameworks such as PEEK may increase the risk of mechanical complications, highlighting the importance of proper screw tightening and regular maintenance protocols.

The difference between the deformation of the framework and the supporting bone (ΔFW–Bone) can be influenced by framework material, internal design, prosthetic configuration, and loading direction. In the present study, this difference ranged from approximately 3–13 μm under vertical loading to 6–17 μm under oblique loading, indicating that lateral forces amplified framework flexibility to a greater extent than bone deformation. Among the designs, Toronto systems demonstrated smaller deformation gaps than bar frameworks, reflecting lower deformation values under the applied loading conditions. This behavior can be attributed to the more continuous and voluminous geometry of the Toronto framework, which enables improved load distribution and reduces stress concentration compared to bar-type designs. In addition, incorporating the gyroid lattice structure reduces overall stiffness, allowing a more gradual redistribution of stresses within the framework. The lower elastic modulus of titanium further contributes to a more balanced stress transfer, explaining the reduced internal stress observed in the Toronto gyroid Ti configuration. When comparing internal designs, both bar-gyroid and Toronto-gyroid frameworks exhibited slightly higher deformation than their solid counterparts; however, the Toronto-gyroid models maintained the lowest framework–bone difference among all gyroid structures. This suggests that the Toronto geometry partially compensated for the lattice architecture’s flexibility under the simulated conditions. The biomechanical behavior of the gyroid frameworks is attributed to their high porosity, which reduces the effective elastic modulus and bending stiffness, thereby increasing the framework’s compliance.Previous studies have demonstrated that the Gibson–Ashby model shows stronger correlation with experimental data at porosity levels above 70%; [51]; however, deviations may occur at moderate porosity levels due to structural heterogeneity and the material’s increased solid-like behavior.The gyroid lattice structure was represented using a homogenized material approach based on the Gibson–Ashby model, rather than explicit geometric modeling. This approach does not capture the anisotropic and bending-dominated behavior of TPMS structures and should be interpreted as a continuum approximation. Therefore, the 60% porosity used in the present study represents a clinically relevant compromise rather than an attempt to maximize analytical model accuracy. As a result, the framework absorbs a smaller portion of the applied occlusal load, leading to redistribution of the load toward the implant–abutment complex. From a mechanical standpoint, this explains the reduction in internal framework stress accompanied by increased stress levels in implant components.Displacement values were used as a supplementary indicator of global mechanical behavior; however, it is acknowledged that bone remodeling is more closely associated with strain. Therefore, future studies incorporating strain-based evaluation may provide further insight into the physiological response of bone.

Owing to its low elastic modulus, PEEK allows greater elastic deflection [47]. Under simulated loading conditions, this higher flexibility was associated with increased framework deformation and greater framework–bone displacement differences.

Overall, the Toronto-gyroid Co–Cr and Ti frameworks demonstrated a more balanced stress distribution and smaller framework–bone deformation differences under the tested conditions; however, these findings should be interpreted in light of differences in prosthetic superstructure materials and the simplified assumptions inherent to finite element modeling. These findings suggest that the gyroid structure, while reducing internal framework stress through increased compliance, redistributes load toward the implant–abutment complex rather than providing a net reduction in system stresses.

These results should be interpreted within the limitations of finite element modeling, including the assumptions of isotropic material properties and static loading conditions. Differences in prosthetic superstructure materials between bar-type (acrylic resin) and Toronto-type (zirconia-based) designs may have influenced system stiffness, framework deformation, and stress transmission; however, these differences were intentionally preserved to reflect clinically realistic conditions.

The assumption of fully bonded interfaces may overestimate system stiffness and underestimate interfacial micromotion, potentially affecting stress transfer and load-sharing behavior under clinical conditions. In addition, static loading represents a simplified scenario reflecting short-term mechanical response, whereas cyclic loading and higher occlusal forces may significantly influence stress distribution and fatigue behavior.

Furthermore, only a single lattice configuration (approximately 60% porosity and 0.8 mm wall thickness) was evaluated, and gyroid lattice structures were limited to metallic frameworks (Co–Cr and Ti). Variations in lattice parameters such as porosity, unit cell size, and gradient distribution may significantly influence biomechanical behavior and should be investigated in future studies.

Conclusions

Within the limitations of this finite element study, bar systemsexhibited higher stress concentrations than Toronto systems, which were associated with lower deformation values under the tested conditions.Gyroid lattice frameworks reduced internal framework stresses compared with solid designs, but slightly increased stresses in the implantabutmentcomplex, indicating load redistribution rather than overall stress reduction. Among the tested materials, PEEK showed the lowestinternal framework stresses but the highest deformation, reflecting greater flexibility under the tested loading conditions without directevidence of clinical instability. In contrast, Co-Cr and Ti frameworks demonstrated lower deformation values, consistent with their higher elasticmodulus. Toronto configurations, particularly Co-Cr and Ti gyroid designs, demonstrated smaller framework-bone deformation differences,suggesting a more uniform stress distribution under the simulated conditions. Oblique loading consistently produced higher stresses thanvertical loading, highlighting the influence of load direction on stress distribution patterns in full-arch implant-supported prostheses.

Abbreviations

3D

Three-dimensional

CAD

Computer-aided design

CAM

Computer-aided Manufacturing

Co–Cr

Cobalt–chromium

CT

Computed Tomography

DICOM

Digital Imaging and Communications in Medicine

E

Elastic modulus

ECC

Error-correcting code

FEA

Finite Element Analysis

FW

Framework

GPa

Gigapascal

HU

Hounsfield Unit

PAEK

Polyaryletherketone

PEEK

Polyetheretherketone

STL

Standard Tessellation Language

Ti

Titanium

TPMS

Triply periodic minimal surface

µm

Micrometer

ΔFW–Bone

Difference between framework and bone displacement

°

Degree

Authors’ contributions

E.Y. conducted the research, collected the data, performedthe data analysis, and drafted the manuscript. N.Ö. contributed to the research process and assisted with data analysis. V.Ş. developed the studyconcept and design, supervised the research, and provided the final critical review of the manuscript.

Funding

This work was supported by Scientific Research Projects Coordination Unit of Kırıkkale University (Project Number: 2025/070).

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

This in vitro study did not require ethical approval as it did not involve human or animal subjects.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.