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Romanian Biotechnological Letters Vol. 22, No. 4, 2017 Copyright © 2017 University of Bucharest Printed in Romania. All rights reserved ORIGINAL PAPER

Romanian Biotechnological Letters, Vol. 22, No. 4, 2017 12706

Finite element method analysis of the stress induced upon the dental

implant by the mastication process

Received for publication, June 25, 2015

Accepted, July 22, 2015

MIHAI BURLIBAŞA1, ANDREEA ANGELA ŞTEŢIU*2, DRAGOȘ GEORGE MARINESCU3, MIRCEA ŞTEŢIU4, ANCA RĂDUCANU5, ANCA TEMELCEA1, NARCIS MARCOV5, VIOREL ȘTEFAN PERIEANU5, LUMINIȚA OANCEA5, NICOLETA MĂRU5, CAMELIA IONESCU5, MĂDĂLINA MALIȚA1, MIHAI DAVID1, RADU COSTEA1, GABRIELA TĂNASE5, LAURA ŞTEF2, GABRIELA BOȚA2, MIHAELA ROMANIȚA GLIGOR2, CARMEN DOMNARIU2, BOGDAN PAVĂL6, LORELAI GEORGETA SFARGHIU6, ILEANA IONESCU5

1Faculty of Midwifery and Nursing, University of Medicine and Pharmacy „Carol Davila” Bucharest, Romania, 2Faculty of Medicine, „Lucian Blaga” University, Sibiu, Romania, 3Elias Hospital Bucharest, Romania, 4Faculty of Engineering, „Lucian Blaga” University, Sibiu, Romania, 5Faculty of Dental Medicine, University of Medicine and Pharmacy „Carol Davila” Bucharest, Romania, 6S.C. DENTALMED COM S.R.L. Brașov, Romania *Address correspondence to: No 2A, Lucian Blaga Street, Sibiu; e-mail: [email protected]

Abstract

The paper analyses the stress and strain in the dental implant caused by the forces generated during the mastication process. The analysis is conducted by computer modelling the dental implant and simulating its distributed stress. Different loadings are considered, related to the axial direction of the implant, so that the complex mastication process can be as well as possible simulated. Through this type of loading the strain developed into the neck-zone of the implant is revealed; this is the risk zone where, in time, stress may induce cracks or fractures in the implant. An up to 254% increase in stress in the case of chewing mastication in comparison with chopping mastication is observed. Bruxism is an aggravating factor that puts tangential stress on the implant, and consequently a concentration of strain at the abutment-implant junction appears, and the loss of the implant may occur. Conclusions regarding the diminution of the strain at the abutment-implant junction are formulated: increasing the implant diameter by 25%, a diminution up to 18% of the strain at the abutment-implant junction is obtained.

Keywords: finite element method, dentistry, teeth modelling, dental implants, mastication.

1. Introduction

In most edentation forms the replacement of the missing masticatory units with dental implants is a procedure increasingly demanded by patients. That is why oral implantology should meet several requirements related to the materials implants are made of that should be tolerated and integrated into the bone tissue, as well as to the shape and dimension of the various systems used, which should be resilient, given the masticatory loads placed on them [1, 2, 3, 4]. The dental implant is the physical substitute for the missing tooth root to which the implant-supported restoration is attached. The occlusal forces developed during the mastication process are transmitted through the implant. Therefore, the morphological- functional correlation between the implant introduced into the bone tissue and the implant-supported restoration should be achieved by an even pressure distribution. Theoretically, the vertical forces applied to dental implants should be evenly and simultaneously distributed

Finite element method analysis of the stress induced upon the dental implant by the mastication process

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through the occlusal surface of the implant-supported restoration [3, 14]. Practically, because of the own masticatory engram, the patient develops variable forces and loadings that may result in the total or partial destruction of the restoration (both the implant and the implant-supported restoration) [1, 3, 5]. Therefore, a complex analysis of the masticatory pattern as well as of the developed forces is necessary in order to better predict the implant-supported restoration endurance [1, 6, 7]. The morphological and clinical characteristics of both edentation and restoration represent important factors that should be considered when deciding the appropriate type of implant. There is a great variety of implants available, especially screw-type implants, and the choice of a particular type, in terms of form, dimension or material, should be compliant with the treatment plan.

Masticatory loadings on the dental arches are consequences of the combined action of the elevator muscles of the mandible, represented by the pairs masseter/pterygoid and temporalis muscles (figure 1) [1, 5, 6, 7].

Figure 1. The action of elevator muscles (F – direction of the developed force. B1, B2 – dento-dental loading.

C – the reaction at the temporomandibular joint for the masseter/pterygoid muscles) – (c) and temporalis muscles – (a) The unit stress recording by FEM (b) [1, 5, 6, 7].

It is well-known that the structure of a body loaded with variable and repeated in time

force can break at a much smaller strain than it is necessary for its breaking in static conditions [8, 9, 10]. Similarly, one may consider the prosthetic restoration endurance, namely the fatigue strength of the implant subject to the repeated action of masticatory cycle forces. We intend to highlight the risk zones of the dental implant by a finite element analysis of the 3D model of the implant.

2. Materials and Methods

The use of FEM in dental implants stress analysis The finite element method (FEM) allows finding approximate solutions for partial

differential equations and for integral equations as well. The solution approach is based on either eliminating the differential equation completely or rendering the partial differential equations into an approximating system of ordinary differential equations, which are then numerically integrated [1, 2, 4, 7, 8, 11].

In engineering it allows for searching static analysis, dynamic or own values cases. For complicated cases, one of them can be used to simplify the model and to solve differential equations on this simplified model [12, 13, 14, 15].

MIHAI BURLIBAŞA, ANDREEA ANGELA ŞTEŢIU, DRAGOȘ GEORGE MARINESCU, MIRCEA ŞTEŢIU, ANCA RĂDUCANU, ANCA TEMELCEA, NARCIS MARCOV, VIOREL ȘTEFAN PERIEANU, LUMINIȚA OANCEA, NICOLETA MĂRU, CAMELIA IONESCU, MĂDĂLINA MALIȚA, MIHAI DAVID, RADU COSTEA, GABRIELA TĂNASE, LAURA ŞTEF, GABRIELA BOȚA, MIHAELA ROMANIȚA GLIGOR, CARMEN DOMNARIU, BOGDAN PAVĂL, LORELAI GEORGETA SFARGHIU, ILEANA IONESCU


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There are three stages involved in FEM analysis: Pre-processing (MODELLING), Processing (NUMERICAL COMPUTATION) and Post-processing (VISUALISING and ANALYSING THE RESULTS).

2.1. Pre-processing (modelling) means the division in finite elements of the mathematical model using dedicated 3D modelling software (SolidWorks, Catia, ProEngineer, SolidEdge, Unigraphics) and imported in CAE software (Ansys, Abaqus, Ls-Dyna etc.), and numerical modelling. We used in our work SolidWorks as dedicated software.

During this stage special procedures are performed to prepare the model geometry depending on the use, materials, execution technology, physical loading phenomenon and structural analysis [13, 14, 16, 17, 18]. The meshing by finite elements of the model is also performed during this stage, resulting in obtaining elementary cells in the geometry of a unit, most often being used three-dimensional elements such as the tetrahedron (with equilateral triangular faces), pentahedron (with equilateral triangular or square faces), or hexahedron (cubic). One of the basic requirements to be met is that the geometry of the basic physical object should be respected, under shape and volume preservation criteria. Another important aspect is related to the physical-mechanical properties of the model components. Particularly, the objects are the dental implant, the compact bone, the trabecular bone, the composite or metallic materials the implant-supported restorations are made of, and the specific loadings given by masticatory forces.

In the present research cylindrical screw-type implants from TEHNOMED S.A [19] are used. The implants are type 2, made of titanium. Three implants of the same length but different diameters are used (figure 2, table 1).

Considering the technical specifications shown in the drawing of the type 2 implant final product (figure 2A), the three dimensional modelling and the discretsation of the model are performed as in figure 3. Dedicated software such as SolidWorks, Catia, ProEngineer, SolidEdge, Unigraphics are used. For studying the mechanical behaviour of any structures, the main goal is to obtain an accurate geometric model. The results of this phase are geometric models in one of the formats, such as: IGES, VDA, STL, DXF, OBJ, VRML and the most accurate CAD format for exporting a 3 D model – ISO G Code was used by us.

Table 1. Specific dimensions for each implant type [19].



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An important aspect of modelling is represented by applying constraints and subject-specific loadings. We will consider the embedding of the implant into the bone tissue in such a way that no translation in all three axes can be possible (figure 4).

Figure 2. A-The execution drawing and technical conditions for the type 2 implant [19]. B-Components of an implant. 1 – the implant body; 2 – the prosthetic abutment; 3 – the fixing screw of the

abutment; 4 – dental crown; 5 – the fixing system (cement).

Figure 3. 3D model of the type 2 implant. (a) 3D model; (b) 3D mesh model.



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Table 2 presents the physical-mechanical characteristics of the titanium alloy (Ti6A14V) the implants are made of to be considered during processing.

Table 2. Physical-mechanical properties of the implant material [2, 14, 20, 21, 19].

Material

Mechanical characteristics

Density [kg/m3]

Young modulus [Mpa]

Poisson coefficient ν

Yield strength [MPa]

Maximum tensile load

[MPa]

Elongation

[%]

Alloy Ti6Al4V 4.51x103 1.11x105 0.35 - 0.36 795 850-860 15-20

Figure 4. The imposed constraints for the dental implant

with the lock of the nodes translations after SL1, SL2, SB surfaces and an axial force application.

2.2. Processing (numerical computation) entails the numerical analysis of the discretised model considering the modelled constraints and using the finite element analysis dedicated software. ANSYS 11 or ABAQUS 6.14 [11] can be used. In our work ABAQUS 6.14 was used as dedicated software. The software permits to analyse the strain and stress state based on the discrete principle and modal analysis using the finite element method. Thus, we determine the strain and stress state when loading the model in static regime. To analyse the stress distribution, the equivalent tension von Mises (ecv) is used, and the program calculates it as a quadratic average of normal stress at the base, middle or top of the finite element when the shear stress are zero [4, 6, 8, 11, 16].

The loading of the model has to consider the active forces that lift the mandible and close the mouth. These forces are generated by the elevator muscles activated in the mastication process [1, 6, 9, 17, 22] such as:

- Temporomandibular muscles pulling the mandible upward and backward at an angle of 60considering the Frankfurt horizontal plane develop forces up to 700 N;



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- Internal pterygoid muscles acting at an angle of 110considering the Frankfurt horizontal plane develop forces up to 400 N;

- Masseter muscles acting at an angle of 97considering the Frankfurt horizontal plane develop forces up to 800 N. During the mastication process, the front teeth loading is bigger due to the smaller

contact area and the molar teeth loading is more uniform as there are more contact points with larger contact areas. This is the reason why we will consider the loading of an implant from the lateral zone (loading distributed on a larger area), and will take into consideration that the fracture risk increases considerably in the frontal area as there is high stress and strain there.

The maximum load in the first molar is about the maximum value of 390 N. The average force at the same level is of 189 N, considering the transversal area of the muscle acting at a given moment and the distance from the mandible condyle [1, 6, 9, 17, 22].

In order to establish the level of the equivalent von Mises unitary stress in the three considered implant types, we will work with the resultant R force of 50 N (light mastication) acting in vestibulo-lingual plane at an α angle of 0o, 30o, 45o, 60o and 90o, as in figure 5.

Figure 5. The loading point and the angle of force F action.

2.3. Post-processing (visualising and analysing the results). For the three types of implants with a reference loading of 50 N, with loading directions of 00-900, and for the characteristics we have considered before, the data from table 3 are obtained. Figure 6 presents the detailed diagram of the loadings for the most inappropriate case – a loading at an angle of 900 of the thinnest implant.



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Figure 6. The Von Mises equivalent stress for a titanium implant, Ф = 3.6 mm; L= 9 mm, for a 50 N masticatory force at a lingual-vestibular angle of 900.

Table 3. The results of loading the implants with a 50 N force at diverse angles in vestibule -lingual plane (xOz).

Forc

e

[N] Stress in

implant

Angle of force α [ o ]

0 30 45 60 90

50

Maximum Von Mises

stress [Mpa]

for type 1 implant

Ф=3.6mm; L= 9 mm

28.0

41.3

56.7

57.2

71.2

Maximum Von Mises

stress [Mpa]

for type 2 implant

Ф=4.0mm; L= 9 mm

25.5

37.7

51.7

61.3

64.9



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Maximum Von Mises

stress [Mpa]

for type 3 implant

Ф=4.5mm; L= 9 mm

22.9

33.8

46.5

55.1

58.3

3. Results and Conclusions The FEM model provides data concerning the stress and strain conditions resulting from

loading an implant. The modelling follows the fabrication drawing of the implant so we can consider it as an accurate copy of the geometric model, without approximations.

The FEM research on the dental implant proves, for all loading types, the existence of a constant stress at the abutment-implant joint level, which severely diminishes the restoration endurance because of the changes or even fractures in the implants neck.

The research allows for the study of a great diversity of implants and spatial loadings by simply running the program and introducing new data.

Another conclusion concerns the types of mastication. In table 3 one can see small values of the Von Mises stress for the vertical load at a 00 angle (chopping mastication type), and an increase up to 254% for the tangential load at a 900 angle (chewing mastication type). A correctly inserted implant means that the loading axis is as close as possible to the vertical axis of the implant, and any irritating spine causing bruxism is eliminated. A recommendation for the dental implant bearer is to usually use chopping type mastication, and to monitor the apparition of nocturnal bruxism, which is a determining factor of tangential loading.

The method emphasises an increase in the implant fatigue strength directly proportional to the increase in the implant diameter. A 25% increase in the implant diameter results in up to 18% diminution in the axial and tangential stress. Therefore the dentist has to choose implant diameters of maximum value, limited only by the bone offer.

4. Acknowledgements

In this article, all the authors have equal contributions. References

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