Design optimization of a functionally graded overlay using FEA

Abstract

Introduction Dental erosions and molar-incisor hypomineralization are two common dental pathologies requiring minimally invasive restorations such as overlays. The currently used restorative materials are diverse and cover a large range of elastic properties: resin composites (E=15-20GPa), polymer infiltrated ceramic networks (E=30-40GPa), leucite reinforced feldspathic ceramics (E=60-80GPa), alumina and zirconia (E=200GPa). Regarding biocompatibility, ceramics are preferred to resin composites that may contain endocrine disruptors. However, the difference in elastic modulus between the overlay in ceramics and the remaining dental tissues creates excessive stresses at the bottom of the restoration, leading to its mechanical failure, which is the first cause of clinical failure for minimally invasive restorations (Morimoto et al. 2016). Teeth are essentially composed of two natural tissues with very different mechanical properties: enamel (E ∼ 40-80 GPa) and dentine (E ∼ 20 GPa) connected by the dentine-enamel junction (DEJ). Over a few micrometers, DEJ shows a gradient of elastic modulus between 20 GPa and 80 GPa and cracks propagating from enamel are naturally stopped in areas close to the DEJ (Wang et al. 2018). With a biomimetic approach and inspired by the DEJ, numerical studies have introduced a functionally graded material (FGM) with a gradient of elastic modulus at the bottom of the restoration (Huang et al. 2007; Du et al. 2013). They showed that the FGM reduced the stresses observed at the bottom of the restoration and increased the resistance of the prosthesis to masticatory loadings. The objective of our study is to use a similar finite element model to optimize the parameters of the FGM and of the adhesive system for an overlay. 2. Methods Finite element analysis was used to analyze stress distribution in a simplified ceramic overlay axisymmetric model using the commercial finite element software Abaqus (Dassault Systems, 2017). The restored tooth is represented by a multi-layered 8mm diameter cylinder indented by a rigid spherical indenter. A frictionless hard contact is imposed between the two parts. A 120N force is applied on the indenter in the direction of the cylinder, that corresponds to an average contact force in the molar region (Figure 1). The bottom of the cylinder is fixed. A tie contact is implemented between all layers, considered as perfectly bonded. The meshed cylinder is composed of 167,200 4-node bilinear elements with reduced integration and hourglass control. This simplified geometry has been used in the literature to quantify experimentally the influence of numerous parameters (especially thickness and mechanical properties of the chosen materials) while leading to clinically relevant fracture modes of the restoration (Dong and Darvell 2003). A dental vitroceramics (E=80 GPa) was chosen for the outer layer because its mechanical properties (hardness and elastic modulus) are close to enamel and prevent the erosion of the opposite tooth. Tobond a ceramic restoration on dentine, dental surgeons classically use the 2-layers bonding system implemented in our model: its bottom layer is an immediate dentine sealing (IDS) with a methacrylate resin (80 mm thick, E=1 GPa) whereas its upper layer is a glass-filled charged luting composite resin which we tested several thicknesses (from 100 mm to 300 mm) and stiffnesses (from E=6.3 GPa to E=15 GPa). All materials, including dentine (E=20 GPa), are modeled with an isotropic and elastic mechanical behavior. Finally, the FGM is considered as a multilayer ceramic material, whose number of layers can vary from 3 to 10 layers of the same thickness. Its range of elastic moduli can vary from 20 to 80 GPa and its proportional thickness between 30% and 70% of the entire restoration. All these parameters are tuned to optimize the stress reduction in the dental restoration. The impact of the FGM for different restoration sizes is also assessed for clinically relevant restoration thicknesses (1-3 mm). 3. Results and discussion Finite element analysis has shown that the more the FGM is discretized the more the stress is reduced. Considering a FGM bonded to dentine and capped by a feldspathic ceramic, the optimal range of elastic moduli for the FGM is 40-80 GPa. The optimal thickness of the FGM related to the entire restoration is half the size of the restoration, furthermore the optimal bonding system is reached with a 200 mm thick resin composite with E=15 GPa. The configuration shown in Figure 1 induces a decrease of 42% of the maximal principal stress in the prosthesis compared to a conventional leucite reinforced feldspathic ceramic restoration for a 2-mmthick restoration (average thickness for inlay/onlay dental restorations). In this configuration, a compromise has been reached while considering the manufacturing constraints of the FGM. Indeed, the objective is to build this material by piling up layers of feldspathic ceramics with controlled microstructure A thickness layer of 250 mm, as chosen in this model, should be achievable using additive manufacturing. Table 1 shows an exponential decrease of the stress at the bottom of the overlay, for both the fully optimized FGM and the feldspathic ceramics, when increasing restoration thickness from 1 to 3 mm. The FGM decreases the stress of about 47% for all restoration thicknesses, which is especially interesting for thin restorations. 4. Conclusions Using this model, optimal parameters have been determined for a functionally graded restorative material. Functionally graded ceramics, showing a gradient of elastic modulus, are interesting on a clinical point of view, because they decrease the stresses at the bottom of the restoration, leading to more resistant and lasting restorations. This decrease is even more significant for thin restorations, hence promoting less invasive treatments of dental tissue losses as recommended by modern dentistry. The perspective is now to optimize the properties of the FGM considering a 3-dimensional structure with geometry representative of a tooth restored with an overlay. A more realistic FE model presented in Figure 2 is developed to study stresses for different FGM configurations.