# Inlay-Retained Dental Bridges--A Finite Element Analysis
## 2 Materials and Methods  
The finite element method attempts to approximate a solution to a problem by admitting that the domain is divided into subdomains or finite elements, with simple geometric shapes and the function of an unknown state variable that is defined around each element. The operation of choosing the number and type of finite elements, corroborated with the division of the domain into several finite elements, is called discretization. When preparing the analysis model, one must take into account that the shape and dimensions of the design influence the accuracy and time of analysis; in this sense, for a given problem, there are several variants of analysis models. Description of the geometric model and finite element modeling was first performed, a stage that includes: modeling of material characteristics, choosing the finite elements and introducing properties, generating the finite element structure, introduction of limit conditions and forces. Analysis and solution of the finite element model involved setting the solving parameters and then visualizing the states and variations of the parameters. Images of molars, canines, premolars and incisors were taken as a reference; their dimensions were made on a scale, according to the dimensions of the molars on computed tomography (CT) images. Based on the mandibular model, the absence of tooth 3.5 was simulated. To simplify the finite element analysis, only the dental elements 3.3, 3.4, 3.6 and 3.7 were preserved from the assembly. For the application of optimal forces to simulate physiological masticatory load, the main muscles of the mastication process, the masseter muscles and lateral and medial pterygoid muscles were taken into account (Figure 1). The average values of masticatory forces vary from individual to individual and are also influenced by food consistency. In this study, we applied an average force value of 220 N in the premolar area and 400 N in the molar area, introduced in the Autodesk Simulation Mechanical 2014 program (2014, San Rafael, California, US). The model was subjected to loading with a vertical force, applied, in turn, on the occlusal surfaces of each element of the dental bridge: both retainers and pontic. The modeling of an inlay-retained dental bridge was performed, with retainers on teeth 3.4 and 3.6 and pontic on 3.5 (Figure 2). The material used for the bridge was a titanium alloy (T16 Al4V) (Dentaurum, Germany). The force was applied first in the contact area of the occlusal surface of the inlay at the level of 3.4, then at the occlusal face of 3.6 and then on 3.5, occlusal surface, simulating the pressure induced by the food fragment during the masticatory act. Figure 1: Variation of forces and moments developed by the masseter pterygoid muscles during the masticatory process (a mastication cycle). Figure 2: The models of the mandible and the bridge. FEM analysis consists of a mesh realization by splitting a solid volume into finite elements of parallelepiped or tetrahedron shape. Each element behaves individually, with the same characteristics as the base material. Depending on the pressure applied to every element, a specific load or temperature will be exerted and transmitted to the adjacent elements through nodes. For an enhanced accuracy of results, a condition was imposed for the mesh realization: the length between two nodes must always be the same. The model was exported to Autodesk Simulation Mechanical 2014 with a file ending in *. * Sat. These files are opened one by one in Autodesk Simulation Mechanical 2014. After determining the type of analysis (static stress), the mesh command was given. Depending on the objectives of the analysis, the used material properties were: modulus of elasticity, Poisson's ratio and density. The values for these parameters were taken from the literature [9] (Table 1). We analyzed the tensions induced as a result of the application of these forces, on each element of the bridge, in the contact areas located between retainers and pontic and also on aument teeth.