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Article

Biomechanical Evaluation of Implant-Supported Three-Unit Bridge Designs and Retention Types in the Atrophic Posterior Maxilla Using Finite Element Analysis

by
Arzu Yüksel Baysal
1 and
Yeliz Hayran
2,*
1
Department of Prosthodontics, Faculty of Dentistry, Tokat Gaziosmanpasa University, Tokat 60100, Türkiye
2
Department of Prosthodontics, Faculty of Dentistry, Bursa Uludag University, Bursa 16059, Türkiye
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(21), 11793; https://doi.org/10.3390/app152111793
Submission received: 15 October 2025 / Revised: 29 October 2025 / Accepted: 4 November 2025 / Published: 5 November 2025
(This article belongs to the Special Issue Implant Dentistry: Advanced Materials, Methods and Technologies)
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Versions Notes

Abstract

Background and Objectives: This study aimed to evaluate the biomechanical behavior of three-unit implant-supported prostheses with different bridge configurations (mesial cantilever, distal cantilever, and pontic) and two types of retention in the atrophic posterior maxilla, through three-dimensional finite element analysis (3D FEA). The focus was on stress distribution in short implants used in pontic and mesial cantilever designs. Materials and Methods: Six 3D finite element models were developed to represent various prosthetic designs and retention mechanisms in a maxillary segment including the first premolar, second premolar, and first molar regions. Type III bone with 8 mm vertical height simulated an atrophic maxilla. Standard implants were placed in premolar areas and short implants in molar regions. A 100 N oblique load at 45° was applied to each unit to simulate masticatory function. Stress distribution was assessed using von Mises and principal stress criteria. Results: The highest implant and crown stress occurred in the cement-retained distal cantilever (100.14 MPa and 329.95 MPa, respectively), while the lowest values were found in the screw-retained pontic model (44.74 MPa and 81.23 MPa). Mesial cantilevers showed intermediate stress levels. Screw-retained designs generally generated lower stresses within implants than cement-retained ones. In cortical bone, stress ranged from 10.25 MPa in the cement-retained distal cantilever to 4.22 MPa in the screw-retained pontic, while trabecular bone showed maximum stress of 1.69 MPa and 0.82 MPa, respectively. Conclusions: Prosthetic design and retention type significantly influenced biomechanical performance. Screw-retained pontic prostheses with short implants in the molar region provided the most favorable stress distribution. When cantilevers are required, mesial extensions are biomechanically more advantageous than distal ones. Short implants can thus be safely used in the posterior maxilla when accompanied by proper prosthetic design and retention type.

1. Introduction

Rehabilitation of the atrophic posterior maxilla presents a significant challenge in implant dentistry due to anatomical and structural constraints. Progressive bone resorption, often accompanied by sinus pneumatization and leads to both vertical and horizontal bone loss, creating a three-dimensional limitation that compromises optimal implant positioning [1]. Moreover, this region is frequently associated with poor bone quality, classified as Type III/IV according to Lekholm and Zarb [2], and insufficient vertical bone height, further reducing primary stability and the overall success rate of implants [3].
To address the limitations associated with dental implants, maxillary sinus augmentation procedures such as sinus lifting and bone grafting are commonly performed to increase available bone volume and enable implant placement. While these procedures are effective, they come with several drawbacks, including high cost, extended treatment duration, patient discomfort, and potential risks such as graft failure, sinusitis, and complications at the donor site [4,5]. Consequently, alternative strategies have been suggested to reduce surgical complexity, notably the use of short implants [6] and cantilevered prosthetic designs [7].
Short implants have gained increasing attention as a viable option for cases with limited vertical bone height in the posterior maxilla [8]. Their use allows for implant placement without the need for extensive bone augmentation procedures, allowing for the restoration of edentulous spans using three-unit bridges with implants placed in the premolar and molar regions [9]. However, the shorter length and reduced surface area of these implants may compromise their load-bearing capacity and increase the likelihood of mechanical complications, especially under unfavorable loading conditions [10]. Therefore, it is essential to assess short implants across various prosthetic configurations to optimize their clinical success. In patients with atrophic maxilla, single-tooth restorations may be considered a preferable option to enhance the long-term survival of implants by minimizing load transfer between units. However, factors such as limited vertical bone height, reduced occlusal space, and insufficient mesiodistal width of the edentulous area may not always allow the placement of individual implants. In such anatomically constrained situations, the use of multi-unit prostheses becomes inevitable for functional and esthetic rehabilitation. Therefore, pontic or mesial cantilever designs can be considered feasible prosthetic alternatives when implant placement is not possible in one part of the edentulous span. In this context, understanding how occlusal loading interacts with prosthetic design becomes crucial.
Implant-supported prostheses in the posterior maxilla experience complex occlusal forces that significantly influence stress distribution within both the prosthetic components and the surrounding peri-implant bone [11]. Excessive or poorly distributed stress may lead to microdamage, marginal bone resorption, and eventual implant failure [12]. The configuration of the implant-supported restorations, particularly the number and distribution of implants, is crucial for achieving effective load transfer [13]. Generally, a wider spread of implants without cantilever extensions is associated with more even stress distribution and fewer mechanical complications [13].
Nevertheless, when anatomical limitations prevent optimal implant placement, cantilever extensions may be required. Although cantilevered prostheses increase mechanical demands and stress concentrations at the implant-abutment interface and in the surrounding bone, several studies have reported clinically acceptable outcomes, especially when biomechanical principles are carefully adhered to [14,15].
In addition to the configuration of the prosthesis, the type of retention used can significantly affect force transmission, retrievability, and biological response. Screw-retained restorations allow easier maintenance and retrievability but may be more susceptible to mechanical issues such as screw loosening or fracture. In contrast, cement retained prostheses often provide better esthetics and a passive fit; however excess cement may lead to biological complications such as periimplantitis [16]. Therefore, selecting an appropriate retention system requires careful evaluation of both mechanical and biological factors.
Clinicians should consider biomechanical challenges when planning implant-supported restorations in the compromised posterior maxilla. The primary objective is to minimize stress concentrations on the implant-abutment-prosthesis complex and surrounding bone to support long-term functional success. Recent digital and biomechanical research has further emphasized the importance of individualized, graftless approaches in the rehabilitation of the atrophic posterior maxilla. Artificial intelligence–assisted and knowledge-based CAD/CAM systems have demonstrated enhanced accuracy in reproducing natural occlusal morphology and optimizing load transfer, underscoring the biomechanical significance of prosthetic design in stress modulation [17,18]. These advancements align with the contemporary paradigm shift toward minimally invasive, graftless protocols using short implants combined with prosthetic designs that effectively balance occlusal forces and preserve peri-implant bone health. Therefore, evaluating the interplay between short implant placement, prosthetic configuration, and retention type through finite element analysis remains highly relevant to current clinical practice in posterior maxillary rehabilitation.
Three-dimensional finite element analysis (3D FEA) has emerged as a valuable and widely used computational tool for evaluating biomechanical behavior in dental implants [19]. It enables detailed simulation of occlusal loading and stress distribution under controlled conditions, offering insights into how various prosthetic designs and configurations influence implant performance.
Although many FEA studies have examined the biomechanical effects of cantilever lengths and implant positioning, there has been limited research into the combined impact of prosthetic design and retention mechanisms, especially in the context of the atrophic posterior maxilla. Moreover, despite their increasing clinical use, the biomechanical behavior of short implants placed in the posterior maxilla under various prosthetic configurations has not been sufficiently investigated.
This study aimed to analyze the biomechanical behavior of three-unit implant-supported prostheses with different bridge configurations and retention types in the atrophic posterior maxilla using 3D FEA. Additionally, the study assessed the stress distribution in short implants utilized in pontic and mesial cantilever configurations.
The null hypotheses of this study were as follows:
(1)
Different bridge configurations (pontic, mesial cantilever, distal cantilever) would not significantly affect the biomechanical behavior of three-unit implant-supported prostheses.
(2)
The type of retention (screw-retained or cement-retained) would not significantly influence the biomechanical behavior of the prostheses.
(3)
The use of short implants in pontic and mesial cantilever designs would not adversely affect the stress distribution or mechanical stability of the implant-prosthesis complex.
This study sought to address a key clinical question: when sinus lifting is not desired or feasible in the atrophic posterior maxilla, which prosthetic configuration and retention type with short implants provides the most favorable biomechanical performance? Answering this question may guide clinicians toward safer, graftless treatment pathways for posterior maxillary rehabilitation.

2. Material and Methods

This study investigated the biomechanical stress behavior produced by different bridge configurations (pontic, mesial cantilever, distal cantilever) and two retention types (screw-retained and cement-retained) in three-unit implant-supported fixed prostheses. Accordingly, von Mises stresses for the implants, abutments, and crowns, as well as the maximum and minimum principal stresses in the cortical and trabecular bone, were evaluated. Furthermore, the stress distribution in short implants specifically used in pontic and mesial cantilever designs was comparatively analyzed.

2.1. Design

A total of six three-dimensional finite element models were constructed to represent various prosthetic configurations and retention mechanisms in the atrophic posterior maxilla. Each model included a segment of the maxillary bone encompassing the regions of the first premolar, second premolar, and first molar. The vertical bone height beneath the maxillary sinus was standardized at 8 mm to reflect the clinical limitations of implant placement without sinus augmentation. The bone structure was modeled as Type III [2], featuring dense trabecular bone surrounded by a 1 mm thick cortical layer. In the present study, the implants, abutments, abutment screws, prosthetic frameworks, and surrounding cortical and trabecular bone structures were modeled as homogeneous, isotropic, and linearly elastic materials, consistent with standard assumptions used in previous FEA investigations [20,21,22]. The periodontal ligament was not modeled as a separate heterogeneous structure [20,21,22]; instead, a uniform 25 µm cement layer was defined in cement-retained models to represent the cement interface. Complete osseointegration was assumed at the bone–implant interface. The abutment–implant and abutment–framework interfaces were modeled as bonded contacts, whereas the screw–abutment–implant interfaces were defined as fixed contacts [20,21,22]. Three different bridge configurations were simulated: (1) distal cantilever: Implants in the first and second premolar regions were used to support a cantilevered molar crown, (2) mesial cantilever: Implants in the second premolar and first molar regions were used to support a cantilevered premolar crown, and (3) fixed-fixed pontic design: Implants in the first premolar and first molar regions were used to support a pontic at the second premolar site. Standard implants of conventional length were placed in the premolar region, while short implants were utilized in the molar region to replicate anatomical limitations. For each configuration, two types of retention were evaluated, screw-retained and cement-retained, resulting in a total of six distinct models.

2.2. Modeling of Implants and Prosthetic Components

Computer software was used to create three-dimensional finite element models. Implants were positioned at various anatomical locations to simulate clinically relevant scenarios. The placement sites for the implants corresponding to each model are summarized in Table 1 and illustrated in Figure 1. To facilitate classification, the odd-numbered models (Model 1, 3, 5) represent screw-retained restorations, while the even-numbered models (Model 2, 4, 6) represent cement-retained restorations.
In this study, the implant and prosthetic components were three-dimensionally scanned using a SmartOptics 3D scanner (Sensortechnik GmbH, Bochum, Germany). The resulting models, obtained in STL format, were imported into Rhinoceros 4.0 software (Robert McNeel & Associates, Seattle, DC, USA). Alignment between the prosthetic components, implant screws, and bone tissues was performed using the Boolean method in Rhinoceros. The dimensions of the dental implants to be placed in the jawbone were determined based on the bone resorption pattern in the implantation area and the anatomical location of the maxillary sinus. Implant sites were prepared while considering both the mesiodistal dimensions and crown lengths of the teeth as specified in Wheeler’s Dental Anatomy Atlas [23] (Table 2), ensuring a minimum inter-implant distance of 3 mm. According to the bone height in the atrophic maxilla, Nobel Biocare™ Parallel Conical Connection RP (Nobel Biocare, Gothenburg, Sweden) dental implants with a diameter of 4.3 mm and length of 13 mm were placed in the first and second premolar (1PM and 2PM) regions. In contrast, implants with a diameter of 5 mm and length of 7 mm were inserted in the first molar (1M) region (Figure 2A).
The abutments used on the implants were modeled as Nobel Biocare™ straight Snappy abutments, measuring 1.5 mm in height for cement-retained fixed prostheses (Figure 2B). For screw-retained systems, Nobel Biocare™ multiunit Plus Conical Connection RP (Nobel Biocare, Gothenburg, Sweden) abutments were also used, with the same height of 1.5 mm (Figure 2C). Nobel Biocare™ titanium Clinical Screws (Conical Connection RP) (Nobel Biocare, Gothenburg, Sweden) were used as abutment screws (Figure 2D), while Nobel Biocare™ titanium Prosthetic Screws (Multi Unit) (Nobel Biocare, Gothenburg, Sweden) were utilized as occlusal screws (Figure 2E).
After finalizing the implant geometry and placement, the corresponding prosthetic superstructures were designed and integrated into the model. Metal ceramic restorations were selected for implant-supported prostheses. During the modeling process, a cobalt chromium alloy (Wiron 99; Bego, Bremen, Germany) was utilized for the substructure (Figure 2F), whereas feldspathic porcelain (Ceramco II; Dentsply, Burlington, VT, USA) was employed for the superstructure (Figure 2G). The metal substructure thickness was set at 0.8 mm, and the porcelain thickness was prepared as 1 mm, considering the crown dimensions [24]. Crown designs were modeled based on Wheeler’s Dental Anatomy Atlas [23].
For cement-retained prostheses, a uniform layer simulating zinc phosphate cement with a thickness of 25 µm was modeled between the Co-Cr substructure and the abutments [25,26]. The periodontal ligament was not modeled as a separate heterogeneous structure [20,21]; instead, the cement layer was represented as a homogeneous, linearly elastic, and isotropic material.

2.3. Mesh Generation and Material Properties

Following the geometric construction of the models using VRMesh software (VirtualGrid, Bellevue, DC, USA), they were exported in STL format and imported into Algor Fempro (Algor Inc., Pittsburgh, PA, USA) for FEA. The STL format, due to its wide compatibility across modeling platforms, ensured lossless transfer of node coordinates between software programs. Upon importing into Algor Fempro, the models were defined as maxillary structures, and material properties were assigned to each component, including elastic modulus and Poisson’s ratio, as detailed in Table 3.
To achieve an accurate representation of complex anatomical geometries and to streamline the mesh generation process, ten-node quadratic tetrahedral elements were employed (VRMesh Studio, VirtualGrid). This element type allows for detailed modeling of curved and irregular surfaces, particularly in areas where high geometric fidelity is essential, thus enhancing the realism of the simulation. As the model complexity increased, the number of elements and nodes was adjusted accordingly, with detailed values for the six different prosthetic configurations provided in Table 4.
Following mesh generation, all models were imported into the finite element analysis software Algor Fempro (ALGOR) for preprocessing. The finite element analyses were performed using a workstation equipped with an Intel Xeon® CPU 3.30 GHz processor, 14 GB RAM, and a Windows 7 Ultimate (Service Pack 1) operating system. The modeling workflow included Rhinoceros 4.0 for 3D modeling, VRMesh Studio for mesh optimization, and Algor Fempro for finite element analysis. Each simulation was completed under consistent numerical conditions to ensure computational stability and reproducibility.
All models used in this study were assumed to exhibit homogeneous and isotropic material properties. The interfaces between abutments and frameworks were defined as bonded (tied) contacts, assuming complete adhesion and no relative micromovement between the surfaces [20]. This simplification has been widely adopted in comparable FEA studies to represent a rigid and stable connection under static loading conditions [20,34].

2.4. Boundary Conditions and Loading

Appropriate boundary constraints were applied to realistically simulate clinical conditions. In all models, the anterior, posterior, and superior surfaces of the maxilla were assigned zero degrees of freedom, fully restricting movement in these areas [35]. This setup allowed for an accurate evaluation of load transfer and stress distribution.
To replicate functional loading, a static oblique force of 100 N was applied at a 45° angle in the palato-buccal direction along the long axis of each implant [36]. A point-loading approach was used, targeting the palatal cusps of each prosthetic unit [34]. In the molar region, the 100 N force was divided equally between the two palatal functional cusps, resulting in 50 N applied to each cusp. In total, a combined oblique load of 300 N was applied across each model [34,37], distributed as follows: 100 N on the functional cusp of the first premolar, 100 N on the functional cusp of the second premolar, and 50 N on each of the two palatal cusps of the first molar.

2.5. Validation and Benchmarking

To verify the validity of the finite element models used in this study, the obtained stress magnitudes and distribution patterns were compared with similar studies published in the literature. Cenkoglu et al. [38] and Batista et al. [39] reported that the highest stresses were concentrated around the implant neck in distal cantilever bridges, whereas lower values were observed in pontic and three-implant designs. In addition, Tuzlali et al. [40] demonstrated that screw-retained restorations produced higher stresses on the abutment, while cement-retained restorations transmitted greater compressive stresses to the surrounding bone. Overall, the stress hierarchy, magnitudes, and distribution areas obtained in the present study were consistent with validated FEA references, supporting the validity of our models.

3. Results

FEA was performed on six different models to assess the von Mises stresses in the implants, abutments, and crowns, as well as the maximum and minimum principal stresses occurring in the cortical and trabecular bone. The stress distribution within the prosthesis, implant, and surrounding bone structures was illustrated using a color-coded scale: red areas indicate high-stress concentration regions, while blue gradients represent areas of minimal stress.
Maximum stress values for each group were recorded from the analysis outputs and summarized systematically in descriptive tables (Table 5, Table 6, Table 7, Table 8 and Table 9). Additionally, the stress values and distribution patterns under oblique loading were illustrated in Figure 3, Figure 4 and Figure 5. The odd-numbered models correspond to screw-retained prostheses, while even-numbered models correspond to cement-retained counterparts, all featuring identical implant positions and prosthetic configurations.

3.1. Models 1 and 2 (Distal Cantilever-1PM-2PM Implants)

In Model 1, the highest von Mises stress was founded at the disto-buccal collar of the 2PM implant, measuring 68.80 MPa. In Model 2, the same region showed an increased stress value of 100.14 MPa. Additionally, both models recorded the highest stress concentrations in the abutments were at the disto-buccal collar of the 2PM abutment, with stress values of 191.15 MPa in Model 1 and 138.12 MPa in Model 2. For the crowns, the maximum stress values were noted at the distal margin of the 2PM crown in both models, with measurements of 115.78 MPa in Model 1 and 329.95 MPa in Model 2.
In the cortical bone, the maximum principal stress was observed at the palatal collar of the 1PM implant in both models, with values of 10.25 MPa in Model 1 and 7.86 MPa in Model 2. The minimum principal stress was found at the distal collar of the 2PM implant, recorded as 23.69 MPa in Model 1 and 22.19 MPa in Model 2. In trabecular bone, the maximum principal and minimum stresses were identified at the buccal collar and distal collar of the 2PM implant, with values of 1.66 MPa and 1.57 MPa in Model 1 and 1.69 MPa and 1.53 MPa in Model 2, respectively.

3.2. Models 3 and 4 (Mesial Cantilever-2PM-1M Implants)

The maximum von Mises stress observed in Model 3 was 63.83 MPa at the mesial collar of the 2PM implant, while Model 4 exhibited a higher maximum of 85.20 MPa at the mesio-buccal collar of the same implant. Within the abutments, the maximum von Mises stresses recorded were 138.09 MPa for Model 3 at the mesio-buccal collar and 112.31 MPa for Model 4 at the implant-abutment junction. In the crowns, the maximum von Mises stresses measured were 123.32 MPa for Model 3 and 106.71 MPa for Model 4, both located at the mesial margin of the 2PM crown.
Regarding cortical bone, the maximum principal stresses were 7.25 MPa for Model 3 and 6.31 MPa for Model 4, occurring at the palatal collar of the 2PM implant. The minimum principal stresses were 12.43 MPa in Model 3 (at the distal collar of the 1M implant) and 13.20 MPa in Model 4 (at the buccal collar of the 1M implant). In trabecular bone, the maximum and minimum principal stresses were 1.17 MPa and 0.85 MPa, respectively, in Model 3 (at the mesio-buccal collar of the 2PM implant), and 1.36 MPa and 1.05 MPa in Model 4 (disto-buccal collar of the 1M implant).

3.3. Models 5 and 6 (Conventional-1PM-1M Implants)

In Model 5, the maximum von Mises stress recorded was 44.74 MPa, located at the buccal collar of the 1M implant. In Model 6, this stress increased to 122.78 MPa at the same region. The abutments showed max von Mises stresses of 112.58 MPa for Model 5 and 119.95 MPa for Model 6, both concentrated around the buccal collar of the 1PM implant. The crowns exhibited maximum von Mises stresses of 81.23 MPa for Model 5 (at the mesio-buccal margin of the 1M crown) and 67.42 MPa (Model 6, buccal margin of the 1M crown).
For cortical bone, maximum principal stresses were 9.01 MPa in Model 5 and 7.08 MPa in Model 6, both located at the palatal collar of the 1PM implant. The minimum principal stresses were 20.38 MPa in Model 5 and 19.94 MPa in Model 6, observed at the distal collar of the 1M implant. In trabecular bone, the maximum and minimum principal stresses were 2.10 MPa and 1.23 MPa, respectively, in Model 5 (at the buccal collar of the 1PM implant), and 1.24 MPa and 1.37 MPa in Model 6 (at the disto-buccal collar of the 1M implant).

4. Discussion

This study aimed to evaluate the biomechanical behavior of three-unit implant-supported prostheses using 3D FEA. The study investigated different bridge configurations, including mesial cantilever, distal cantilever, and pontic designs, alongside two types of retention in the atrophic posterior maxilla. Additionally, it examined the stress distribution in short implants utilized in pontic and mesial cantilever designs.
The findings demonstrated that both prosthetic design and retention significantly affected the stress distribution within the implants, abutments, crowns, and surrounding bone structures. Models with distal cantilever exhibited the highest stress concentrations, while the pontic design allowed for the most favorable load distribution. Moreover, there were notable differences between screw-retained and cement-retained restorations. When comparing distal cantilevers, the use of short implants in pontic and mesial cantilever designs resulted in a more favorable stress distribution across the implant, abutment, crown, and both cortical and trabecular bone, indicating a biomechanical advantage for both retention types. As a result, the first two null hypotheses were rejected, while the third, stating that the use of short implants in pontic and mesial cantilever designs would not adversely affect the stress distribution or mechanical stability of the implant prosthesis complex, was accepted.
During functional loading, the stresses generated in implant-supported fixed prosthetic restorations are transmitted through the superstructure to the implant and the surrounding supporting tissues. When excessive occlusal forces are applied, they can lead to increased mechanical stress at the implant-bone interface, potentially disrupting the physiological balance of bone modeling and remodeling. This disruption may result in marginal bone loss and, over time, could contribute to early implant failure [41].
In addition to their biological effects, occlusal overloads can also cause mechanical failures within the implant prosthesis assembly, impacting the longevity of the restoration. Mechanical complications such as implant fracture, abutment screw loosening or fracture, and prosthetic component failure have been frequently reported as clinical consequences of occlusal overload [42]. Given that stress distribution within the peri-implant bone and prosthetic components is a key factor in the long-term success of implant-supported restorations, biomechanical evaluations play a crucial role in guiding clinicians toward optimal treatment planning. This is particularly important in anatomically compromised areas such as the posterior maxilla. A comprehensive understanding of implant biomechanics is essential to ensure durable and functionally stable prosthetic outcomes.
In this study, FEA, a widely accepted and reliable biomechanical simulation method, was employed to evaluate stress distribution in dental implants and the surrounding peri-implant structures [19]. FEA offers significant advantages by replicating complex clinical conditions in implant dentistry, allowing the simulation of various anatomical, material, and loading configurations under controlled and reproducible parameters [43].
Due to the intricate three-dimensional morphology of the maxillary region and the materials involved, a three-dimensional linear static analysis was conducted. This approach provides more realistic and clinically relevant results compared to two-dimensional models [44]. Building upon these methodological strengths, the current study applied static oblique loading to assess how different prosthetic designs influence biomechanical responses under functional conditions. Static loading is commonly used in the literature to simulate functional masticatory forces in implant-supported rehabilitations and is regarded as adequate for comparative biomechanical evaluations [29,38]. Based on these established methodological principles, the loading conditions were defined in accordance with previous FEA studies to ensure physiological relevance.
The loading protocol in this study was established based on previous finite element analyses of occlusal force magnitude and direction in the posterior maxilla. Applying chewing forces at a 30–45° oblique angle to the vertical axis has been shown to generate realistic stress patterns in cortical bone and represent clinical occlusal loading [36,45,46]. For multi-unit or cantilevered prostheses, loads should be distributed among multiple functional units to reproduce actual occlusal contact and prevent unrealistic stress concentration [19]. Forces between 100 and 300 N correspond to functional mastication, while loads above 1000 N reflect parafunctional activity [37]. Accordingly, in this study, 100 N at 45° was applied to the functional cusps of the first and second premolars, and the 100 N on the first molar was divided equally between its two palatal cusps (50 N each), totaling 300 N across the bridge. A point-loading approach was adopted to idealize occlusal contacts and enable consistent comparison among models, as previous research indicates similar overall stress trends between point and distributed loads, with point-loading offering better control and reproducibility [19,34,47].
To enhance the accuracy and resolution of the simulation, this study utilized a higher number of elements and nodes than typically found in previous FEA research. This increase in mesh density improved the reliability of the stress distribution data [48,49]. However, as is often necessary in finite element modeling, certain simplifications were made due to computational limitations and the need for standardization. For instance, bone tissue was assumed to be homogeneous, isotropic, and linearly elastic, and a fully osseointegrated implant-bone interface was modeled [50]. While these assumptions do not fully capture the complex, anisotropic, and dynamic nature of bone physiology, where the mechanical properties vary according to direction and the stress–strain relationship is nonlinear, and biological behavior evolves over time [51], they provide a consistent framework for comparative mechanical evaluation. In isotropic modeling, materials are characterized by uniform mechanical properties in all directions, defined by two constants: elastic modulus and Poisson’s ratio [19,52]. All material properties used in this study were selected based on validated data from the literature [24,27,33,50].
In this study, the anterior, posterior, and superior surfaces of the maxilla were fully constrained to ensure numerical stability and prevent rigid body motion. This approach has also been employed in previous finite element studies on the atrophic maxilla [22,35]. Although this configuration may result in a slightly stiffer overall response and reduced total displacement, the constrained areas were located far from the peri-implant region; therefore, it was anticipated that they would not introduce significant artifacts in the local stress distribution.
According to the bone density classification by Lekholm and Zarb, Type III and IV bone qualities are the most common in the posterior maxilla [2]. Therefore, in our study, a Type III bone structure was modeled for the posterior maxilla, consisting of dense trabecular bone surrounded by 1 mm of thin cortical bone [24,53]. To simulate a moderately atrophic maxilla, a setting of 8 mm was used.
Implant dimensions were selected according to established clinical guidelines, with 7 mm × 5 mm short implants placed in the first molar region and 13 mm × 4.3 mm standard implants positioned in the premolar area [54,55]. Short implants were preferred primarily due to their reduced surgical invasiveness and enhanced clinical success, particularly in the atrophic posterior maxilla, where vertical bone height is insufficient due to maxillary sinus pneumatization, making sinus augmentation unfeasible [56,57,58].
To ensure the long-term success of short implants, critical factors include prosthetic design and retention type. A balanced consideration of biomechanical, biological, esthetic, and economic aspects is essential [9]. During normal masticatory function, occlusal forces are rarely purely axial; they are generally exerted in an oblique direction. Juodzbalys et al. [59] demonstrated that the direction of applied force significantly impacts stress distribution, with stress levels varying by as much as 85% depending on the angle [46]. Oblique loading is widely accepted as a more realistic simulation of functional loading conditions because it incorporates axial, lateral, and bending components. Compared to purely axial forces, oblique loading generates higher stress concentrations within the cortical bone [60]. Consequently, several researchers, including Geng et al. [19], have recommended the inclusion of oblique forces in static finite element analyses to enhance clinical relevance. In line with this, our study adopted oblique occlusal loading to provide a more accurate biomechanical representation.
The material properties assigned in the analysis are crucial for accurately determining stress distributions. In this study, maximum and minimum principal stress values were used for brittle materials such as bone, while von Mises stress values were employed for ductile materials like titanium and metal, as they are considered more appropriate and provide a safer estimation of failure risk [29]. Since the results obtained from FEA are based on deterministic mathematical calculations without variability, statistical analysis is not applicable. Therefore, the calculated stress values and their distributions were evaluated and interpreted descriptively.
Numerous studies have demonstrated that short implants yield long-term success rates comparable to those of standard implants in the atrophic posterior maxilla [57,58,61]; however, this success is not solely dependent on implant length. Prosthetic design and retention type are also critical determinants, as they directly influence load transmission to the implant and surrounding bone structures. Cantilever extensions and retention mechanisms can significantly alter the direction and magnitude of forces, thereby affecting biomechanical equilibrium [9,19]. This study aimed to evaluate the biomechanical impact of various three-unit bridge configurations (pontic, mesial, and distal cantilever) and two types of retention (cement retained and screw retained) on stress distribution using 3D FEA.
According to the results of this study, distal cantilever designs produced the highest von Mises stress values in the implant, abutment, and crown components for both retention types. Pronounced stress concentrations were observed in the second premolar region, particularly around the implant, abutment, and crown. This finding is consistent with previous studies reporting that distal cantilevers, due to their longer lever arms, transmit greater stresses to both prosthetic components and the supporting bone structures [38,39]. In contrast, pontic (fixed-fixed) designs exhibited the lowest stress concentrations, with values noticeably lower than those observed in the cantilever models. Previous studies have similarly reported that fixed implant-supported bridges incorporating a pontic offer a more balanced and favorable stress distribution compared to cantilevered designs [38,39,62,63]. Even when short implants are used in the molar region, the fixed-fixed pontic configuration provides a more homogeneous and balanced stress distribution across both premolar and posterior areas, thus appearing biomechanically superior and clinically suitable for implant-supported rehabilitations in the atrophic posterior maxilla. These results highlight the critical influence of bridge configuration on biomechanical load distribution.
Consistent with the present outcomes, previous numerical analyses by Doğanay et al. [64], Yu et al. [65], and Zhong et al. [66] also reported similar biomechanical tendencies regarding the effects of cantilever length and implant distribution. Although these authors focused on mandibular models, they reported similar biomechanical tendencies regarding the effects of cantilever length and implant distribution. Doğanay et al. demonstrated that increasing cantilever length and distal offset amplified bending moments and compressive stresses around the implant neck region, whereas distal implant positioning that eliminated cantilever extensions reduced stress transmission within peri-implant bone. Similarly, Yu et al. [65]. and Zhong et al. [66] emphasized that avoiding posterior cantilevers and increasing the anteroposterior distribution of implants improved load transfer and reduced mechanical complications. Despite the anatomical differences between the mandible and the atrophic maxilla, the present results confirm the same trend, showing that shorter lever arms and mesial extensions provide a more favorable load distribution and minimize stress concentration in the posterior maxilla, where cortical support is thinner and trabecular bone predominates.
Extending these observations to the atrophic maxilla, Fan et al. [67] evaluated the influence of mesial cantilever extensions on stress, strain, and screw loosening in implant-supported prostheses with distally tilted implants. They reported that mesial cantilever configurations did not significantly increase stress levels in implants or bone but enhanced screw preload stability, suggesting a more balanced load transfer. Similarly, Aboelfadl et al. [68] compared mesial and distal offset designs in the atrophic posterior maxilla and found that distal cantilever extensions produced the highest von Mises stresses in both implants and peri-implant bone, whereas fixed-fixed (pontic) designs showed the most homogeneous stress distribution. These observations are in strong agreement with the present study, confirming that mesial cantilever and pontic restorations distribute occlusal loads more evenly than distal extensions and thus represent biomechanically safer options for rehabilitating the atrophic posterior maxilla. When retention type was considered, screw-retained and cement-retained systems demonstrated distinct biomechanical behaviors that further influenced stress transfer within the implant–prosthesis complex.
Beyond the influence of bridge design, when comparing screw-retained and cement-retained systems, screw-retained restorations tended to exhibit lower von Mises stress values within the implants. Due to their rigid structure, screw-retained prostheses are less prone to bending deformation than cement-retained restorations [33]. Nissan et al. reported that cement-retained restorations transmit higher loads to the implant neck because of increased bending moments [69]. The lower stress values observed in screw-retained models, as well as the higher stresses in cement-retained systems, can be attributed to the reduced bending tendency and more homogeneous stress distribution of screw-retained designs, while cemented restorations create greater bending moments that transfer additional loads to the implant neck. Mechanical failure occurs when the von Mises stress exceeds the yield strength of the implant material (550 MPa) [29]. In this study, the stress values for both screw-retained and cement-retained restorations remained below this threshold.
In screw-retained models, higher von Mises stress values were generally observed in the abutments and crowns compared to the implants. Similarly to the present findings, Tuzlali et al. reported that screw-retained systems exhibited greater von Mises stress in the abutments than cement-retained systems [40]. The authors suggested that cement acts as a stress-dissipating medium at the abutment-implant interface. Given that stresses generated during functional loading in implant-supported fixed prostheses are transmitted through the superstructure to the implant and surrounding supporting tissues, the lower von Mises stress values noted in the abutments of cement-retained restorations in this study may result from the stress-dissipating effect of the cement layer, which acts as a separating interface between the abutment and the prosthetic structure.
Principal stress values are typically used for brittle materials such as cortical bone. The tensile strength of cortical bone is approximately 100 MPa, while its compressive strength is around 173 MPa [70]. According to the results of this study, both tensile (max. principal) and compressive stresses (min. principal) in the cortical bone for all restorations remained below these critical thresholds. In both cortical and trabecular bone, the lowest tensile and compressive stress values were generally observed around the implant neck region in cement-retained models. Previous studies have suggested that the cement layer may compensate for interfacial discrepancies within the underlying structure and thereby contribute to a more uniform load distribution throughout the bone-implant-restorative system [71,72]. The finding that screw-retained restorations produced higher stress values in both cortical and trabecular bone compared to cement-retained types is consistent with previous mechanical studies [73,74,75]. These biomechanical findings suggest that optimizing load distribution through proper retention and bridge design can help maintain peri-implant bone integrity in the atrophic maxilla.
From a clinical standpoint, the present study provides evidence-based guidance for prosthetic planning in the atrophic posterior maxilla, where sinus augmentation is not feasible. Integrating our FEA findings with recent clinical data on short implants [8,76], the following decision rules are proposed: (a) When possible, fixed–fixed (pontic) designs should be preferred over cantilevers. This configuration yielded the most favorable peri-implant stress distribution in our models and is supported by clinical evidence showing fewer mechanical complications and higher survival rates for short implants compared with standard-length implants in graftless conditions. (b) When cantilevers are unavoidable, mesial cantilever extensions are biomechanically preferable to distal ones. Our analysis demonstrated lower stress transmission to the distal implant and surrounding bone in mesial configurations, which can help preserve peri-implant bone and enhance long-term success. (c) For short implants, screw-retained restorations are recommended, as they reduce stress at the implant–bone interface. However, they may transfer greater stress to the abutment or crown complex; thus, clinicians should schedule regular maintenance visits for screw-tightening and occlusal adjustment [76]. Recent clinical and systematic findings further support these biomechanical observations, indicating that short implants exhibit high survival rates and no significant difference in complication rates compared with standard-length implants [8]. These insights collectively provide clinicians with practical, evidence-based strategies to plan predictable, graftless rehabilitations in compromised posterior maxillary sites.
This study has certain limitations inherent to FEA. Bone was modeled as a homogeneous, isotropic, and linearly elastic material, which does not fully represent its complex biological behavior. The implant–bone interface was assumed to be completely osseointegrated, excluding the possibility of micro-movement or partial integration. Loading was applied under static conditions and did not reflect dynamic or fatigue loading seen in clinical function. These simplifications were adopted to ensure computational efficiency and to facilitate comparison of relative stress magnitudes among different models.Although cortical bone exhibits anisotropic behavior and biological tissues show viscoelastic or fatigue responses that are not fully captured in static linear analyses, these effects were beyond the scope of the present FEA model. Additionally, screw preload was not simulated in this model, meaning that torque-induced clamping effects and potential preload loss at the implant-abutment interface were not represented. Only one bone quality (Type III) and a fixed bone height were simulated, which limits generalizability to other anatomical scenarios. Implant positions and prosthetic components were ideally aligned, which may differ from real-life clinical variability. Furthermore, the study did not explore contact nonlinearity at interfaces or variations in occlusal schemes, both of which can influence load distribution and implant biomechanics in vivo.
Future studies should address these limitations by employing patient-specific models with anisotropic bone properties, frictional and nonlinear contact conditions, and dynamic or fatigue loading protocols to simulate real occlusal forces more accurately.

5. Conclusions

Prosthetic design and retention type significantly affected the biomechanical performance of implant-supported restorations. The screw-retained fixed implant-supported prosthesis with pontic designs incorporating short implants in the molar region demonstrated the most favorable biomechanical performance. When the use of cantilevers was necessary, mesial extensions were found to be biomechanically more advantageous than distal ones. Therefore, it can be concluded that short implants can be safely placed in the molar region when the appropriate prosthetic design and retention type are selected.

Author Contributions

Conceptualization, A.Y.B. and Y.H.; Methodology, A.Y.B.; Investigation, A.Y.B.; Data Curation, A.Y.B. and Y.H.; Writing—Original Draft Preparation, A.Y.B.; Writing—Review and Editing, A.Y.B. and Y.H.; Visualization, A.Y.B.; Supervision, Y.H.; Project Administration, Y.H. All authors have read and agreed to the published version of the manuscript.

Funding

The study was financed by grant No. 2020/08 from Tokat Gaziosmanpasa University scientific research projects.

Data Availability Statement

The data can be obtained from the authors upon request.

Acknowledgments

The authors would like to express their gratitude to Ay Tasarim Co., Ltd. (Ankara, Turkiye) for performing the finite element analysis of this study.

Conflicts of Interest

The authors declare no conflicts of interest and no affiliation with, or representation of the products evaluated in this study.

Abbreviations

The following abbreviations are used in this manuscript:
3DThree-Dimensional
Co-CrCobalt–Chromium
FEAFinite Element Analysis
MPaMegapascal
NNewton
μmMicrometer
mmMillimeter
D3Type III Bone
CADComputer-Aided Design
CAMComputer-Aided Manufacturing
STLStandard Tessellation Language

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Figure 1. Finite element models illustrating implant locations and prosthetic configurations for each group. M: Abbreviation for model.
Figure 1. Finite element models illustrating implant locations and prosthetic configurations for each group. M: Abbreviation for model.
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Figure 2. Modeled Implants and Prosthetic Components. (A) Implants (B) Snappy abutment (C) Multiunit abutment (D) Abutment screw (E) Occlusal screw (F) Co-Cr framework (G) Feldspathic porcelain.
Figure 2. Modeled Implants and Prosthetic Components. (A) Implants (B) Snappy abutment (C) Multiunit abutment (D) Abutment screw (E) Occlusal screw (F) Co-Cr framework (G) Feldspathic porcelain.
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Figure 3. (A) Von Mises stress distributions (MPa) for implants in models M1–M2 (distal cantilever). (B) Von Mises stress distributions (MPa) for implants in models M3–M4 (mesial cantilever). (C) Von Mises stress distributions (MPa) for implants in models M5–M6 (pontic). M: abbreviation for model.
Figure 3. (A) Von Mises stress distributions (MPa) for implants in models M1–M2 (distal cantilever). (B) Von Mises stress distributions (MPa) for implants in models M3–M4 (mesial cantilever). (C) Von Mises stress distributions (MPa) for implants in models M5–M6 (pontic). M: abbreviation for model.
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Figure 4. Von Mises stress values (MPa) and distribution patterns of the crowns. M: abbreviation for model.
Figure 4. Von Mises stress values (MPa) and distribution patterns of the crowns. M: abbreviation for model.
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Applsci 15 11793 g005aApplsci 15 11793 g005bApplsci 15 11793 g005c
Figure 5. (A) Maximum and minimum principal stress values (MPa) in the cortical bone for models M1–M2. (B) Maximum and minimum principal stress values (MPa) in the trabecular bone for models M1–M2. (C) Maximum and minimum principal stress values (MPa) in the cortical bone for models M3–M4 (D) Maximum and minimum principal stress values (MPa) in the trabecular bone for models M3–M4. (E) Maximum and minimum principal stress values (MPa) in the cortical bone for models M5–M6. (F) Maximum and minimum principal stress values (MPa) in the trabecular bone for models M3–M4. M: abbreviation for model.
Figure 5. (A) Maximum and minimum principal stress values (MPa) in the cortical bone for models M1–M2. (B) Maximum and minimum principal stress values (MPa) in the trabecular bone for models M1–M2. (C) Maximum and minimum principal stress values (MPa) in the cortical bone for models M3–M4 (D) Maximum and minimum principal stress values (MPa) in the trabecular bone for models M3–M4. (E) Maximum and minimum principal stress values (MPa) in the cortical bone for models M5–M6. (F) Maximum and minimum principal stress values (MPa) in the trabecular bone for models M3–M4. M: abbreviation for model.
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Table 1. Distribution and placement of implants according to prosthetic design models.
Table 1. Distribution and placement of implants according to prosthetic design models.
ModelScrew RetainedModelCement Retained
1 C–2PM–1PM2C–2PM–1PM
3 1M–2PM–C41M–2PM–C
5 1M–P–1PM61M–P–1PM
1PM: first premolar; 2PM: second premolar; 1M: first molar; P: pontic; C: cantilever.
Table 2. Mesiodistal dimensions and crown heights of teeth (mm).
Table 2. Mesiodistal dimensions and crown heights of teeth (mm).
ToothCrown HeightMesiodistal Width
1PM8.57
2PM8.57
1M7.510
Table 3. Mechanical properties of materials used in the study.
Table 3. Mechanical properties of materials used in the study.
MaterialElastic Modul
(Gpa)		Poisson’s
Ratio		References
Titanium1100.35[24,27,28,29]
Cortical Bone13.70.3[24,27,29,30,31]
Trabecular Bone (D3)1.370.3[24,28,31]
Cobalt-Chromium Alloy2180.33[24,27]
Feldspathic Porcelain82.80.35[24,27]
Zinc Phosphate Cement22.40.25[32,33]
All implant, abutment, and screw components were modeled as titanium.
Table 4. Number of elements and nodes for each prosthetic configuration.
Table 4. Number of elements and nodes for each prosthetic configuration.
ModelNumber of ElementsNumber of Nodes
11,961,319369,617
21,635,192319,779
31,623,964310,393
41,303,485256,903
51,562,741305,012
61,303,231256,612
Table 5. Von Mises stress values (MPa) for implants.
Table 5. Von Mises stress values (MPa) for implants.
Model1PM2PM1MPeak Location
119.3668.80C2PM disto-buccal collar
251.77100.14C2PM disto-buccal collar
3C63.8333.822PM mesial collar
4C85.2083.522PM mesio-buccal collar
528.54P44.741PM buccal collar
6103.97P122.781M buccal collar
1PM: first premolar; 2PM: second premolar; 1M: first molar; P: pontic; C: cantilever.
Table 6. Von Mises stress values (MPa) for abutments.
Table 6. Von Mises stress values (MPa) for abutments.
Model1PM2PM1MPeak Location
1120.92191.15C2PM disto-buccal collar
280.57138.12C2PM disto-buccal collar
3C138.0973.312PM mesio-buccal collar
4C112.3147.472PM mesio-buccal collar
5112.58P90.642PM buccal collar
6119.95P57.731PM buccal collar
1PM: first premolar; 2PM: second premolar; 1M: first molar; P: pontic; C: cantilever.
Table 7. Von Mises stress values (MPa) at the marginal areas of crowns.
Table 7. Von Mises stress values (MPa) at the marginal areas of crowns.
Model1PM2PM1MPeak Location
173.41115.78C2PM distal
241.02329.95C2PM distal
3C123.3292.632PM mesial
4C106.7160.692PM mesial
558.97P81.231M mesio-buccal
657.44P67.421M buccal
1PM: first premolar; 2PM: second premolar; 1M: first molar; P: pontic; C: cantilever.
Table 8. Maximum principal and minimum principal stress values (MPa) in the cortical bone.
Table 8. Maximum principal and minimum principal stress values (MPa) in the cortical bone.
Model1PM (Max/Min)2PM (Max/Min)M (Max/Min)Peak Location
110.25/1.797.08/23.69C1PM palatal collar/2 PM distal collar
27.86/2.916.46/22.19C1PM palatal collar/2 PM distal collar
3C7.25/10.594.60/12.432PM palatal collar/1PM distal
4C6.31/9.923.08/13.202PM palatal collar/1M buccal
59.01/8.95P4.46/20.381PM palatal collar/1M distal
67.08/7.17P3.77/19.941PM palatal collar/1M distal
1PM: first premolar; 2PM: second premolar; 1M: first molar; P: pontic; C: cantilever.
Table 9. Maximum principal and minimum principal stress values (MPa) in the trabecular bone.
Table 9. Maximum principal and minimum principal stress values (MPa) in the trabecular bone.
Model1PM
(Max/Min)		2PM
(Max/Min)		M
(Max/Min)		Peak Location
11.38/0.701.66/1.57C1PM buccal collar/2PM distal collar
20.70/0.571.69/1.53C1PM buccal collar/2PM distal collar
3C1.17/0.720.90/0.852PM mesiobuccal collar/1M distobuccal collar
4C1.36/0.560.59/1.052PM buccal collar/1M distobuccal collar
52.10/0.35P0.69/1.231PM buccal collar/1M distobuccal collar
61.24/0.48P0.65/1.371PM buccal collar/1M distobuccal collar
1PM: first premolar; 2PM: second premolar; 1M: first molar; P: pontic; C: cantilever.
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Yüksel Baysal, A.; Hayran, Y. Biomechanical Evaluation of Implant-Supported Three-Unit Bridge Designs and Retention Types in the Atrophic Posterior Maxilla Using Finite Element Analysis. Appl. Sci. 2025, 15, 11793. https://doi.org/10.3390/app152111793

AMA Style

Yüksel Baysal A, Hayran Y. Biomechanical Evaluation of Implant-Supported Three-Unit Bridge Designs and Retention Types in the Atrophic Posterior Maxilla Using Finite Element Analysis. Applied Sciences. 2025; 15(21):11793. https://doi.org/10.3390/app152111793

Chicago/Turabian Style

Yüksel Baysal, Arzu, and Yeliz Hayran. 2025. "Biomechanical Evaluation of Implant-Supported Three-Unit Bridge Designs and Retention Types in the Atrophic Posterior Maxilla Using Finite Element Analysis" Applied Sciences 15, no. 21: 11793. https://doi.org/10.3390/app152111793

APA Style

Yüksel Baysal, A., & Hayran, Y. (2025). Biomechanical Evaluation of Implant-Supported Three-Unit Bridge Designs and Retention Types in the Atrophic Posterior Maxilla Using Finite Element Analysis. Applied Sciences, 15(21), 11793. https://doi.org/10.3390/app152111793

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