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. 2024 Dec 30;24:1572. doi: 10.1186/s12903-024-05373-5

Finite element analysis on implant-supported bar with different geometric shapes

Peerakan Kupprano 1, Krid Kamonkhantikul 1, Woraporn Homsiang 2, Hidekazu Takahashi 3, Mansuang Arksornnukit 1,✉
PMCID: PMC11684229  PMID: 39736666

Abstract

Background

The selection guideline for the implant-supported bar connectors (ISBC) of hybrid denture is lacking. This study investigated the maximum von Mises stress (vMS), stress distribution, and displacement of various geometric ISBC in mandibular hybrid dentures, as well as the maximum principal stress (σmax) in the acrylic resin part, through finite element analysis.

Methods

Four different geometric cross-sectional patterns for mandibular ISBC—L, Y, I, and Square—of equal volume, based on the “All-on-4” concept, were created. Titanium alloy was used for ISBC with an acrylic resin wraparound. Models were integrated into the software and loading simulations mimicking mastication forces on posterior teeth in centric and eccentric loadings were performed. vMS was used for ISBC assessment, and σmax was assessed in acrylic resin.

Results

In centric loading, vMS was mainly at the distal screw channel across most ISBCs. Y ISBC showed the least vMS, while I and Square ISBC demonstrated uniform stress distribution on both sides; load and non-load-bearing sides. The others showed concentrated vMS only on the load-bearing side. Square ISBC exhibited the most displacement. In the acrylic resin region of each, σmax was found concentrated around the contact point between two adjacent denture teeth at different locations, with Square showing the highest σmax. Under eccentric loading, the maximum vMS of each model was found at the interface between the distal screw channel and the lingual aspect of the abutment, with comparable vMS. Square ISBC experienced the most significant displacement and showed the highest σmax within the acrylic resin juxtaposed with the screw channel.

Conclusion

The Y model of titanium-alloy in mandibular ISBC demonstrated the lowest vMS and displacement.

Keywords: Implant-supported bar connectors, All-on-4, Finite element analysis, Dental implants

Background

Fixed detachable prostheses, also known as hybrid dentures or fixed complete dentures, offer an effective solution for rehabilitating edentulous patients. This treatment modality involves placing multiple implants to support a hybrid denture, leading to enhanced function, aesthetics, and overall improved quality of life for edentulous patients [1, 2]. The success rate of hybrid dentures was impressively high, with a 99.2% implant survival rate and a 92.1% prosthesis survival rate over five years [3]. However, prosthesis complications were more frequently observed than biological complications [4]. Various factors contribute to the success and durability of hybrid dentures, such as the quantity and distribution of dental implants, surgical techniques, and the selection of prosthesis design and material [5, 6].

In hybrid dentures, the implant-supported bar connector (ISBC) is the primary structure that connects all prosthesis components to the implants, ensuring stability and support by evenly distributing forces through the abutments. To perform this role effectively, the ISBC should be rigid and passively fit to distribute masticatory forces [7]. Titanium alloy, cobalt-chromium, zirconia, and polyetheretherketone were commonly used for fabricating ISBCs [1, 7–10]. It was demonstrated that titanium, gold and silver-palladium ISBC exhibited similar low von Mises stress (vMS) [11]. Among the available designs, a metal-supported bar with wraparound acrylic resin was widely used [12, 13]. Various cross-sectional designs for ISBCs were also available, selection often influenced by brand and the familiarity of the dentist or technician with specific designs.

Finite element analysis (FEA) is a non-destructive numerical method used extensively to simulate and study the mechanical behavior of systems under different conditions. This computational method, which divides structures into finite elements, has been applied in engineering and dentistry to evaluate material performance and effectiveness of design [14, 15]. Most FEA studies on rehabilitating edentulous patients with dental implants have been focused on implant fixture configuration and angulation [16–19]. While some studies examined the biomechanical behavior of full-arch implant-supported restorations, with emphasis on the implant-bone interface [17, 20–22] and implant-abutment connection [23, 24] rather than the prosthesis’s part through FEA. Study of stress distribution and pattern on the prosthetic components, particularly the different geometric shape of ISBC, is lacking. Therefore, this piece of information will complete the spectrum of hybrid denture.

ISBCs in hybrid dentures are like structural beams in engineering, as both serve as load-bearing elements. Sufficient strength and rigidity in maintaining structural integrity under bending are required to effectively support and distribute loads. Different cross-sectional designs provide varying levels of flexural strength and resistance to deformation [8, 10]. For instance, I-beams are commonly used in buildings and bridges as horizontal structural elements, while rectangular beams or square beams are often found in residential construction. L-beams serve as braces and support, while Y-beams, a modified form of triangular beam, are widely used in bridges and towers due to their efficient load-carrying capacity with reduced weight [25, 26].

A key concept in beam mechanics is the “area moment of inertia” also known as the “second moment of inertia”. This quantity represents the sum of squared distances of differential area elements from the neutral axis of a beam’s cross-section, indicating how material is distributed relative to this axis. This distribution directly affects a beam’s resistance to bending and overall structural integrity. The neutral axis, where no compressive or tensile stress occurs under bending, is crucial for strengthening beams. Increasing the area moment of inertia by distributing material farther from the neutral axis enhances the ISBC’s strength [25, 26].

However, the forces transmitted on dental prostheses differ from those in structural engineering, and the knowledge of optimal ISBC designs for hybrid dentures is still missing. Currently, there is no consensus on the optimal design for ISBCs in hybrid dentures. Therefore, this study aimed to examine the maximum vMS, stress distribution, and displacement across four different geometric cross-sectional configurations of ISBC in mandibular arch, as well as the maximum principal stress (σmax) in the acrylic wraparound part of each, through FEA under two loading conditions: centric and eccentric. The null hypothesis was that four configurations of titanium mandibular ISBC, with equal cross-sectional areas, were not different in terms of stress, stress distribution, and displacement.

Methods

FEA models mimicking mandibular superstructure consisted of four multi-unit abutments (Astra Tech Multibase Abutment EV; Dentsply Dental GmbH, Bensheim, Germany), four bridge screws (Astra Tech Multibase EV Bridge Screw; Dentsply Dental GmbH, Bensheim, Germany), and the implant-supported bar connector (ISBC). The anterior screw channels were positioned between the lateral incisor and canine, while the posterior screw channels were located between the second premolar and first molar. Four different cross-sectional geometrics for the mandibular ISBC were created—L-type (L), Y-type (Y), I-type (I), and Square-type (S)—all models were set to have a perfect interface with the abutments and bridge screws. Four ISBC designs shared equal volume with cross-sectional area of 9 mm². All models had an anterior-posterior (A-P) spread of 18.5 mm and a cantilever length (CL) of 18.5 mm, achieving an optimal CL/AP ratio of 1 [27]. The vMS criterion was used to analyze across the four different ISBC configuration designs, while the σmax was used to explore the acrylic components [28]. A comprehensive analysis of both ISBC and acrylic components was conducted by combining qualitative observations, quantitative calculations and transformed into color coded for visualization.

Hybrid denture modelling

The superstructure models, consisting of multi-unit abutments, bridge screws, with four different cross-sectional geometric of mandibular ISBC were created using Computer-Aided Design (CAD) software (SolidWorks©; Dassault Systèmes SolidWorks© Corp., Concord, MA, USA). All models were scaled based on actual components. All the parts were positioned following the “All-on-4” concept [29]. The arch dimensions, determined by averaging measurements from edentulous mandibular arch subjects, were 46 mm in width and 50 mm in length [30]. The wraparound component, which included the acrylic denture teeth and gingival part, was constructed to warparound the entire ISBC (Fig. 1).

Fig. 1.

Fig. 1

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The black color shows the cross-sectional pattern of ISBC in prosthesis model, with each cross-sectional area being 9 mm². A-D L, I, Y, and S, respectively

Meshing

The entire prosthesis model, including all components, was imported into FEA software (Ansys 19.2; ANSYS Inc., Canonsburg, PA, USA) for analysis. For meshing, a 10-node tetrahedral element was selected. The node and element count for each model are provided in Table 1.

Table 1.

Nodes and elements count in each model

Model Nodes Elements
L 1,841,752 1,285,917
I 1,841,496 1,285,936
Y 1,816,077 1,276,158
S 1,820,451 1,281,465
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Loading scenarios and boundary conditions

Titanium alloy was selected as ISBC material, and the wraparound material was acrylic resin. The specific mechanical properties of these materials are detailed in Table 2. Boundary conditions were set to be fixed at the bottom flat surface of all abutments. This excluded the connection between abutments and implants to simplify the superstructure evaluation with the intention to focus on structure of hybrid denture and to eliminate the confounding factors such as different implant-abutment connection [16–19], the shape, size and angulation of implant [23, 24], or bone type [31, 32]. Since the bonding between alloy and acrylic resin could not be assumed, therefore, the connection between the ISBC and acrylic resin was defined as frictional, a coefficient of friction of 0.25 [33] was selected, indicating mechanical interlocking between the two materials. Bilateral loading forces were applied sequentially in centric loading to simulate masticatory forces on the teeth. A maximum biting force of 700 N [34] was applied to the occlusal surface of all teeth in the centric loading scenario to differentiate the responses of each ISBC design. In the eccentric loading scenario, a 700-N force was applied unilaterally to the buccal incline plane of the buccal cusp of the canine and premolar teeth at a 45-degree angle to the occlusal plane.

Table 2.

Mechanical properties of materials [35]

Component Material Young’s modulus Poisson’s ratio
Wraparound part Acrylic resin 2.94 GPa 0.3
Abutment, Bridge screw Titanium 110 GPa 0.35
Supported bar connector Titanium 110 GPa 0.35
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Results

Centric loading conditions

The computed maximum vMS of each model was I > L > S > Y (Fig. 2). The maximum vMS was found ventrally on the load-bearing side at the distal aspect of the distal screw channel across all evaluated ISBC models, except for Y, where the maximum vMS occurred dorsally on the load-bearing side. The maximum vMS of all ISBCs was found on both the distal screw channel, extending progressively toward the cantilever arm (Fig. 3). The I and S ISBCs demonstrated similar stress distribution patterns, marked by uniform stress dispersion across both load-bearing and non-load-bearing sides (Figs. 3B and D). Conversely, the L and Y ISBCs exhibited a more concentrated stress distribution on the load-bearing side (Figs. 3A and C).

Fig. 2.

Fig. 2

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Maximum vMS of four models of ISBC in centric loading conditions. Actual values from FEA were on the top of each bar

Fig. 3.

Fig. 3

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vMS (MPa) of the ISBC in centric loading conditions. A-D L, I, Y, and S, respectively. The small red arrow indicated the area of maximum vMS. The green arrow indicated the direction of the load

The most significant displacement occurred at the most distal part of the cantilever, with S > L > Y > I (Fig. 4). The I and S ISBCs experienced maximum displacement on the load-bearing side, while the others showed maximum displacement on the non-load-bearing side (Fig. 5).

Fig. 4.

Fig. 4

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Maximum displacement of four models of ISBC in centric loading conditions. Actual values from FEA were on the top of each bar

Fig. 5.

Fig. 5

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Displacement (mm) of the framework in centric loading conditions. A-D L, I, Y, and S, respectively. The red arrow indicated the area of maximum displacement. The green arrow indicated the direction of the load

At the wraparound component, the σmax level was S > L > I > Y (Fig. 6). The color coded of σmax revealed distinct patterns of stress concentration across different models, specifically at the contact point of different adjacent teeth. The σmax was between the second premolar and first molar in L (Fig. 7A). The I and Y exhibited their σmax between the lateral incisor and canine (Figs. 7B and C). Meanwhile, the S demonstrated σmax at the juncture between the canine and premolar (Fig. 7D).

Fig. 6.

Fig. 6

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σmax stress of four models of acrylic wraparound in centric loading conditions. Actual values from FEA were on the top of each bar

Fig. 7.

Fig. 7

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σmax (MPa) of the wraparound part in centric loading conditions. A-D L, I, Y, and S, respectively. The small red arrow indicated the area of peak of σmax

Eccentric loading conditions

The maximum vMS followed the order: L > I > S > Y. The differences of maximum vMS of all IBSCs were marginal. This could be assumed as comparable (Fig. 8). Maximum vMS position of all ISBCs was found at the lingual aspect of distal screw channel on the non-load-bearing surface of the loading side (Fig. 9). vMS primarily concentrated at mesial and distal screw channels and ventral side of the bar connecting the two screw channels on the non-load bearing surface of the loading side.

Fig. 8.

Fig. 8

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Maximum vMS of four models of ISBC in eccentric loading conditions. Actual values from FEA were on the top of each bar

Fig. 9.

Fig. 9

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vMS (MPa) of the ISBC in eccentric loading conditions. A-D L, I, Y, and S, respectively. The small red arrow indicated the area of maximum vMS

The maximum displacement magnitude followed the order S > Y > L > I (Fig. 10). Among the ISBCs, this displacement was observed at the most distal lingual aspect of the cantilever bar on the loading side (Fig. 11).

Fig. 10.

Fig. 10

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Maximum displacement of four models of ISBC in eccentric loading conditions. Actual values from FEA were on the top of each bar

Fig. 11.

Fig. 11

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Displacement (mm) of the ISBC in eccentric loading conditions. A-D L, I, Y, and S, respectively. The red arrow indicated the area of maximum displacement. The green arrow indicated the direction of the load

Within the wraparound part, the S demonstrated the highest σmax compared to the others (Fig. 12). The σmax occurred at the interface between the distal screw channel and the acrylic part, except for the S, where the maximum σmax was found at the interface between the mesial screw channel and the acrylic part (Fig. 13).

Fig. 12.

Fig. 12

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σmax of acrylic wraparound in eccentric loading condition of four models. Actual values from FEA were on the top of each bar

Fig. 13.

Fig. 13

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σmax (MPa) of the wraparound part in eccentric loading conditions. A-D L, I, Y, and S, respectively. The red arrow indicated the area of maximum displacement. The green arrow indicated the direction of the load

Discussion

vMS criterion, widely used to evaluate stress in ductile materials like metals, was applied in this study to analyze titanium ISBCs. Among the designs, the Y ISBC consistently demonstrated the lowest maximum vMS under both centric and eccentric loading conditions (Figs. 2 and 8). Additionally, displacement analysis revealed that the Y and I ISBCs had the lowest and equivalent displacement values (Fig. 4).

The engineering principles underlying these findings are explained by two key equations:

Deflection equation:

D=Wa2×3L-a/6EI

where D is the deflection of a beam at a specific point resulting from a load W applied at a distance a from one end of the beam, L represents the total length of the beam, E is the modulus of elasticity, and I is the area moment of inertia of the beam’s cross-section; and

Bending stress equation:

σ=M×y/I

where σ is the bending stress at any point in the beam’s cross-section subjected to a bending moment M, and y is the distance from the neutral axis to the point where the stress is being calculated.

The area moment of inertia, representing the sum of squared distances of differential area elements from the neutral axis, emerged as a critical factor in the ISBC’s mechanical behavior. All ISBCs in this study had standardized cross-sectional areas. However, the Y ISBC’s superior material distribution farther from the neutral axis resulted in the highest area moment of inertia under centric loading conditions. This minimized deflection and bending stress, leading to the lowest maximum vMS and displacement, making it the most mechanically efficient design for hybrid dentures.

Under eccentric loading, set at a 45-degree angle from the occlusal plane, the neutral axis shifted compared to centric loading conditions. As a result, all ISBCs exhibited comparable maximum vMS due to their equal mass distribution relative to the neutral axis, resulting in similar area moments of inertia except S due to the shorter distance of differential area elements from the neutral axis.

These findings underscored the importance of the area moment of inertia in influencing mechanical performanced and highlighted its significance in selecting an optimal ISBC design for hybrid dentures.

Designs with the higher area moments of inertia could provide dental professionals with the options that offer longevity of prosthesis. Increasing the area moment of inertia can be achieved by distributing materials away from the neutral axis, which requires additional restorative height that may be limited by the available restorative space, or by increasing the cross-sectional area of the ISBC, resulting in a heavier restoration. Increased weight is often overlooked in dentistry, potentially posing challenges in available space for positioning teeth and increasing laboratory costs. Meticulous planning and adjustments are essential to harmonize aesthetics with functionality, favoring designs that distribute material away from the neutral axis, as demonstrated in the Y design.

The uniform stress distribution along the I and S ISBCs (Fig. 3B and D) might be attributed to their symmetrical configurations. According to the bending stress equation, when the ISBC was loaded on the load-bearing side, it underwent compression on load-bearing side and tension on the non-load-bearing side. In I and S ISBCs, both compression and tension sides had similar distance from the neutral axis, resulting in equal stress magnitudes but different types of stress. This uniform stress distribution pattern was observed on both load-bearing and non-load-bearing sides. In contrast, L and Y ISBCs showed greater stress distribution on the load-bearing side due to their neutral axis located toward non-load-bearing side.

For the acrylic component, σmax, a key indicator for evaluating brittle materials and reflecting tensile stress in the acrylic-based region, aligned with the displacement of the ISBC models (Figs. 4 and 6), This observation stemmed from the lack of bonding between the acrylic and the ISBC, characterized as frictional in this study. Despite of application of metal primer or silane coupling agent, the improvement in bond strength would be vanished after 20,000-cycle thermocycling [36]. Moreover, there was no effect on bonding of cast titanium with acrylic resin with the presence/absence of the silane [37]. It was hypothesized that poor bonding between metal and wraparound part would lead to the inferior physical properties as in metal wire mesh reinforced glass epoxy composites [38]. Therefore, neither ISBC nor acrylic resin in this study strengthened each other. Stress concentration in acrylic parts was primarily found at the contact point of certain adjacent teeth (Fig. 7), supporting the observation that failures of acrylic wraparound ISBCs in hybrid dentures often occurred at these locations [4]. Employing milling technology to create denture teeth as monoblock could enhance the structural integrity of the acrylic elements in such restorations. In eccentric loading conditions, the S model exhibited σmax concentration at the interface between the mesial screw channel and the acrylic wraparound with the highest value, differing from the others (Fig. 13). It was hypothesized that the σmax in the S model exceeded the mechanical interlocking threshold at the distal screw channel, let to the shift stress concentration to the mesial screw channel. To alleviate this effect, sandblasting and applying an appropriate metal primer might enhance the longevity of the prosthesis by increasing bonding between metal and acrylic [39, 40]. But this effect might be transient after thermocycling [36].

In this study, a loading force of 700 N, an average maximum biting force of natural teeth on gnathodynamometer, was applied [34]. This was intended to clearly demonstrate the possible responsive effects of different components under high loading force. The lower force might hinder some responsive characteristics which could not be clearly differentiated between each ISBC. The result of this present study could possibly provide information as a selection guideline for the framework of mandibular hybrid dentures. By comprehensively understanding the performance of various ISBCs under diverse loading conditions, the shapes and designs that enhanced the durability and efficacy of dental prostheses could be properly selected, thereby mitigating the risk of failure. The findings of the present study suggested that, when an equal amount of metal used, the Y ISBC exhibited the highest performance. Therefore, the null hypothesis was rejected. The limitations of this study included several simplifications made for calculation purposes. Specifically, it was assumed that the abutment was fully connected to the implant with maximum constraint, and factors such as implant design, bone structure, and abutment-implant connection were excluded from the evaluation. This was because such confounding factors might affect the outcomes. Future studies on a more comprehensive mandibular model with different implants, different abutment and connection designs with Y ISBC were recommended.

Conclusion

Within the limitations of this study, it was suggested that among four different geometric cross-sections of titanium alloy ISBCs with equivalent volume on four implant supported hybrid denture for mandibular arch, the Y model demonstrated the lowest stress level and the least bending.

Acknowledgements

This research was supported by the Second Century Fund (C2F), Chulalongkorn University.

Authors’ contributions

PK, KK and MA contributed to conceptualization, methodology, formal analysis, writing—original draft. PK contributed to model construction, data acquisition and analysis. WH and HT contributed to critically revised manuscript. All authors contributed to manuscript revision, read, and approved the final version of manuscript.

Funding

Not applicable.

Data availability

The data sets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

The data sets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

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