Dental implants must sustain the mastication loads exerted on natural teeth. These repetitive forces can cause implant loosening or failure that require extraction and replacement of the defective implant. Peri-implantitis affects up to 20% of patients (Mombelli et al., 2012) and is a is a notable cause of implant failure. Peri-implantitis is characterized by an infection of the gingival soft tissue that can then propagate to bone and cause its resorption, which in turn increases the likelihood of mechanical implant failure. The long-term stability of dental implants is strongly determined by the osseointegration process. Formation of bone at the implant’s surface results in establishing a load transfer mechanism between the implant and the surrounding bone (Li et al., 2020). Incorporating porosities in a dental implant increases the contact surface area with bone and thus represents a promising strategy to improve long-term stability. Bony ingrowth inside pores creates a mechanical interlocking between the two structures (Pałka and Pokrowiecki, 2018). Alternatively, the failure risk of dental implants can be reduced by using porous implants as drug-delivery devices: their pores can be loaded with antibiotics to treat locally infections such as peri-implantitis (De Cremer et al., 2017).

The production of complex implant geometries such as porous structures was enabled by the development of metal additive manufacturing (AM) (Hao et al., 2016). Titanium has been the predominantly used material for dental implants due to its advantageous properties in terms of biocompatibility, resistance to corrosion and osteoinductivity (Haugen and Chen, 2022). Titanium has also been used to develop porous scaffolds for dental and orthopaedic applications (Lv et al., 2021). The introduction of porosities in implants reduces mechanical strength relative to their solid counterparts and their mechanical behavior depends not only on the porosity level but also on the pore geometry (Maconachie et al., 2019; Chen et al., 2020). The mechanical properties of a wide range of porous configurations have been determined by testing scaffolds under both monotonic (Soro et al., 2019; Xiong et al., 2020) and fatigue loads (Li et al., 2016; Dallago et al., 2018; Lietaert, 2018).

Dental implants must comply with the ISO 14801 standard to ensure sufficient mechanical strength. This standard describes the mechanical testing procedure to determine endurance limit, i.e., the load level at which the implant has an infinite lifetime, i.e., it will not fail during its intended usage period. The prescribed bending-compression fatigue loading mode mimics the cyclically applied forces caused by mastication. However, a high number of samples (N ≥ 15) per design are required and the experiments are time-consuming with a single test lasting up to 4 days. Although several studies have investigated the failure of conventional implants in this testing configuration (Shemtov-Yona and Rittel, 2014; Song et al., 2017; Rojo et al., 2018; Velasco-Ortega et al., 2019), only a few have focused on porous implants (Wang et al., 2019; Vanmunster et al., 2022; Lovera-Prado et al., 2023). Most studies investigating porous dental implants utilized monotonic tests in a variety of loading modes such as uniaxial compression, bending-compression, three-point bending and pull-out (Chakraborty et al., 2020; Huang et al., 2020). These tests have the advantage of being quicker than fatigue testing while allowing a qualitative comparison of different designs but may not be relevant for the fatigue failure required by the ISO 14801 standard.

The design process of implants is an iterative process requiring several prototypes. However, testing multiple porous configurations according to ISO 14801 is costly and time consuming and hence the appeal of developing alternative methods to quickly compare the fatigue life of multiple designs has arisen. Finite element (FE) modeling is a promising approach that meets this criterion and has been widely used to simulate the mechanical behavior of biomedical (Taylor and Prendergast, 2015; Lewis et al., 2021; Panagiotopoulou et al., 2021) and dental (Trivedi, 2014; Reddy et al., 2019) implants. Previous studies have utilized FE simulations to model ISO 14801 testing of conventional dental implants (Prados-Privado et al., 2018; Lee et al., 2021), but only a single study has modeled the ISO testing of a porous dental implant with a single pore design (Wang et al., 2019). The design process requires the evaluation of several configuration. Although the effect of unit cell geometry and porosity on the uniaxial fatigue strength of porous scaffolds has been studied both in vitro and in silico (Zheng et al., 2018; Maconachie et al., 2019; Benedetti et al., 2021), the impact of porous configuration has not been investigated for porous dental implants under bending-compression prescribed by the ISO 14801 standard. Therefore, the aim of this work is to develop, calibrate, and validate an FE-based tool to predict the fatigue life of 3D-printed porous titanium specimens mimicking dental implants.

We have established and validated a computational workflow to predict the endurance limit of porous specimens directly from their CAD models (Figure 1). Specifically, the tool uses CAD-based FE models to predict the monotonic failure load for various pore types and porosities and, consecutively, the fatigue life (i.e., endurance limit) based on empirically established relationships.

Calibration of the tool was performed by establishing three relationships. First, the differences between planned CAD-based and printed geometries were evaluated with micro computed tomography (µCT) image analysis and conversion rules were determined. Second, experimental testing was performed to establish the link between fatigue and monotonic behaviors. Lastly, FE simulations were performed to predict the ultimate load and correlate it with the experimental ultimate load. Calibration was achieved in a series of experiments involving four specimen groups of different pore types and porosities. The workflow was then validated on two other specimen groups with different porosities.

The FE simulation approach developed and calibrated in this study was found to accurately predict an implant design’s infinite fatigue life for a validation set having different porous configurations. This prediction tool can be an efficient surrogate for time consuming fatigue testing directly based on CAD models and therefore accelerate the development process of porous implants. This approach can also be utilized as a benchmark to evaluate the fatigue strength of different porous configurations under bending-compression loading corresponding to the ISO 14081 standard.

Another finding of this study was that monotonic testing appeared to be a good surrogate of fatigue testing. The normalized fatigue life curves (Figures 8B,C) were consistent for all designs and, most importantly, the endurance limits were reached at the same normalized load level range of 10%–15% of F u l t . From an implant development perspective, this result shows the potential of monotonic testing to be used for rapid screening of several designs, enabling the selection of the most promising designs to be tested cyclically, reducing the number of time-consuming fatigue tests.

The normalized endurance limit determined in this work was significantly lower than that of solid titanium ( σ e / σ y ≈ 40%) (Amin Yavari et al., 2013). This discrepancy was most probably caused by manufacturing imperfections such as surface roughness and irregular strut thicknesses where fatigue crack initiation is more likely to occur (Dallago et al., 2018; Benedetti et al., 2021). Several studies reported that porous titanium structures have a lower fatigue resistance than solid titanium. Vanmunster et al. tested a porous dental implant under ISO 14801 conditions and reported an endurance limit equal to 14.7% of F u l t (Vanmunster et al., 2022). Both Lietaert et al. and Amin Yavari et al. determined the S-N curves of porous cylinders under uniaxial compressive loading (Amin Yavari et al., 2013; Lietaert, 2018). Extrapolating the fatigue failure relationships reported by them to 5 million cycles results in fatigue limits ( σ e ) of 7.7% and 16.4% of σ y , respectively. These values are consistent with the normalized endurance limit determined in the present work.

The fact that the experimental ultimate monotonic load was found in this study to be a good surrogate of endurance limit supports our initial choice to simulate the monotonic test with the FE models. With this approach, only one parameter ( u u l t p l ) was needed to be calibrated experimentally. Modeling the fatigue behavior would have presented the advantage of establishing a direct link between the simulations and the experimental fatigue behavior. The feasibility of this approach was demonstrated by the implementation of fatigue algorithms for porous cylinders (Hedayati et al., 2016; Zargarian et al., 2016) and conventional dental implants (Tsai et al., 2013; Prados-Privado et al., 2018; Lee et al., 2021). However, implementing this was beyond the scope of the present study since, among other challenges, characterizing the fatigue properties of the printed material would have been necessary and the complexity of the model would have increased. Similarly to the present study (Wang et al., 2019), combined ISO 14801 experimental testing of a porous dental implant with FE modelling. They simulated an implant integrated in a mandibular cross-section and loaded monotonically 30° off-axis. This configuration did not reproduce accurately the experimental test but allowed a qualitative comparison, with their porous implant showing higher stress levels in silico and a shorter fatigue life in vitro than the solid one.

Three strategies that were employed in this study to define the FE geometry for each design. Utilizing the original CAD design is generally the most convenient approach since it does not require any additional characterization of the printed samples. Hence, most in silico studies modelled porous dental implants with as-designed CAD geometries (Wang et al., 2019; Huang et al., 2020; Zhang et al., 2020). The ultimate loads computed with this method, however, did not correlate significantly (p = 0.12) with the experimental results (Figure 9). In addition, the worst prediction was achieved with this geometry during model validation, with the ultimate load of 50SW being underestimated by 23% (Figure 10). This discrepancy may be explained by the different printability of the two unit cell types. The µCT analysis revealed that the printed porosities were lower than for the CAD-based planned geometries, by approximately 4% for SP and 16% for SW. For the same CAD-based planned porosity, F u l t exp was higher for SP than for SW (Figure 7), confirming the contribution of the extra printed material to the mechanical strength of the resulting. porosity shows that SP has a higher strength. Thus, 50SP and 60SW have similar printed porosities (Figures 6–b) but the ultimate load of 50SP is superior by 60%.

The µCT-based modeling approach provided predictions that correlated well with experimental data (R² = 0.98) since it incorporated the real geometry of the samples. Simulating four scanned samples per design showed reasonably small variability of the estimated ultimate loads (Figure 9). These models took into account manufacturing irregularities that reduce the mechanical strength of porous titanium scaffolds as highlighted by Liu et al. (2017). For example, stress concentrations can be caused by an irregular strut thickness, while aggregates of partially fused particles on the surface contribute less to structural stiffness (Figure 6A). However, this approach cannot be used in the optimization workflow in a prospective manner aiming to predict the endurance limit of new porous configurations without the necessity of manufacturing. Adjusting the CAD geometry provided a good compromise between the exact representation of the printed geometry and a CAD-generated geometry that is suitable for the purposes of a numerical predictive workflow. For all designs, adjusted CAD-based FE models exhibited higher ultimate loads than µCT-based ones, although these should be similar in the case of an ideal adjustment. This difference is most likely caused by the lack of irregularities of the adjusted CAD geometry. This optimal repartition of the same volume of material results in a higher predicted monotonic strength.

This study has a number of limitations that should be addressed. First, this workflow was able to predict the endurance limit for porous configuration variations, but its validity was not assessed for other design features such as the overall dimensions of the implant (diameter, length) or the position and shape of the porous region. The fatigue strength of an implant could, for example be enhanced by adding solid elements to stiffen structure. Such approach was adopted by (Xiong et al., 2020), who optimized the strength of a porous implant in uniaxial compression by varying the diameter of a solid central rod. Adapting the method developed here to a full implant design may require a partial recalibration of some parameters, e.g., the plastic failure displacement. The monotonic failure criterion was defined here based on displacement and not stress. A stress-based failure criterion would be independent from the global sample geometry and would consist in predicting strut failure. However, Benedetti et al. reported that the failure mode of a porous structure was dependent of unit cell topology and can result in different degrees of ductility (Benedetti et al., 2021). Lastly, the scope of ISO 14801 limits the pore locations that can be investigated with the current method. The part of the sample starting 3 mm below nominal bone level and therefore all implant features below the embedding plane are not considered in these tests. Since the purpose of porous dental implants is primarily to increase osseointegration, many designs reported in the literature (Obaton et al., 2017; Yang et al., 2017; Hong et al., 2020) incorporate pores located in this “blind spot”. As such, alternative methods have been employed to test these designs, either experimentally (e.g., three point bending, uniaxial compression) (Chakraborty et al., 2020; Huang et al., 2020; Xiong et al., 2020), or numerically (e.g., simulating the implant’s behavior in bone) (Liu et al., 2017; Zhang et al., 2020).

In conclusion, a fatigue life prediction tool for porous dental implants was developed, calibrated, and validated in the present study possible by combining in vitro and in silico methods. Fatigue and monotonic mechanical testing were performed on six porous configurations of a simplified implant design. The monotonic failure load was found to be a good and efficient surrogate of the fatigue failure load, with the endurance limit of all designs being situated between 10% and 15% of the monotonic ultimate load. FE simulations predicted well the experimental monotonic test results when the model geometry was based on µCT images, but not for as-designed CAD-based model geometries. This approach ignores the discrepancies between CAD and printed geometries. This limitation was resolved by utilizing CT-based geometry or by adjusting the porosity of the CAD model.