Paper submission
Mechanical Analysis of Extracoronal Magnetic Attachment using
Three-dimensional Finite Element Method
Yo. Ohno, R. Kanbara, Y. Nakamura, T. Masuda, H. Kumano, K. Hayashi, H. Nakamura, T.
Iwai, Y. Takada1, Y. Tanaka
Department of Removable Proshodontics, School of Dentistry Aichi-Gakuin University
1
Division of Dental Biomaterials, Tohoku University Graduate School of Dentistry

Introduction
Magnetic attachments were originally developed to apply for non-vital teeth. Plastic patterns
for extracoronal attachments were developed to expand clinical applications including vitalteeth. In clinical setting, a load is indirectly transmitted to the inferior part of extracoronalmagnetic attachments through housings with groove joints. Therefore, a load is applied not only
to the neck of extracoronal magnetic attachments, but also to grooves and housing joints.
Although Shoji from the Department of Removable Prosthodontics, School of Dentistry,
Aichi-Gakuin University, reported the results of strength test of extracoronal attachments withhousings in 20th Japanese Society of Magnetic Applications in Dentistry, there is no theoreticalvalidation. Our department has performed the elastic stress analysis of extracoronal magneticattachments. However, the mechanism of plastic deformation remains to be elucidated.

Objective
The purpose of the present study was to investigate the mechanical strength of extracoronalmagnetic attachments using a three-dimensional finite element method to compare the resultswith the actual measurement data. The housing with joints was attached to extracoronalmagnetic attachments.

Materials and Methods
Preliminary experiment to verify elastoplastic analysis and main experiment to verify
extracoronal magnetic attachment were performed. Analysis models were fabricated for eachexperiment, and boundary condition and material constant were determined. The procedure isshown below. Patran was used for model fabrication and result display, and a general purpose
nonlinear structure analysis solver program (Marc 2008, MSC software) was used for theanalysis.
1. Analysis model1) Preliminary experiment
The simple cubic model with a cross-section area of 1.73 x 1.73 mm and 6.11 mm on

a side was constructed for the preliminary experiment using Patran. The design andanalysis model are shown in Fig. 1.

Fig. 1. Preliminary experiment model2) Main experiment
The 12-mm-high and 9-mm-wide foundation replaced by a natural tooth and anextracoronal magnetic attachment produced from CAD data of the GIGAUSS EC
keeper tray were fabricated as a unit, and 2.0-mm-high and 8.6-mm-wide housing wasattached on the top. After constructing the foundation and extracoronal magnetic model
as a unit, a keeper was cemented, followed by housing placement. Figure 2 shows thedesign and analysis model.

Fig .2. Main experiment model2.

Boundary condition
A complete constraint was applied to the left surface in the X, Y, and Z directions for bothpreliminary and main experiments as is shown in the figure. For loading condition, a column
with 1 mm in diameter was placed on the center of an extracoronal magnetic attachment at
0.5 mm / mm for 15 seconds to apply a load more than 1000 N (Fig. 3).

Fig .3. Boundary condition
3. Material constant
The Young’s modulus and Poisson’s ratio were introduced to SUSXM 27, a material of akeeper and a magnet, and cementum. The analysis model of a preliminary experiment, thefoundation of the main experiment, and 12Wt% Au-Ag-Pt alloy, a material of an
extracoronal magnetic attachment were determined by the stress-strain curve (Fig. 4). Since
the material constant of 12Wt% Au-Ag-Pt alloy is unknown in the actual measurement data,
hardening and softening heat treatment stress-strain curves were introduced to reproduce
elasto-plasticity.
Elastic deformation after each heat treatment was calculated from the linear part of thegraph, and Young’s modulus 12,987 was introduced. An arbitrary figure in the graph wasintroduced after plastic deformation for reproduction (Fig. 5).

Fig .4. Material Properties

Fig .5. Hardening and softening heat treatment stress-strain curves(12Wt% Au-Ag-Pt alloy)

Results

1. Preliminary experiment
Verification of elasto-plastic analysis was performed by actual measurement and loaddisplacement curve. The figure shows a load displacement curve. The X axis stands for thez axis displacement of the preliminary experiment analysis model, and the Y axis stands
for the stress value applied on the test sample of the preliminary experiment. Values in theload displacement curve after hardening and softening heat treatment of the metal wereapproximated the actual measurements (Fig. 6).

Fig .6. Actual measurement and load displacement curve
2. Main experiment1)

Stress distribution

Stress distribution was evaluated using von Mises stress. Stress concentration wasobserved in the upper margin of the extracoronal attachment groove. The result confirmedthat stress is transmitted to the upper and lower margins of foundation (Fig. 7).

Fig .7. Stress distribution

2)

Load displacement curve

The horizontal axis of the load displacement curve shows z axis displacement of an
extracoronal magnetic attachment, and the vertical axis shows a load in the measurement
point shown in the slide.
The result confirmed that plastic deformation occurs over 733 N in the hardening heat
treatment and over 390 N in the softening heat treatment (Fig. 8).

Fig .8. Load displacement curve

Discussions
1. Analysis model
The finite element model used in the main experiment was fabricated by constructing
extracoronal attachment model based on the practically-used and normalized CAD data,and a housing and foundation were fabricated to fit the model. Since the size of the modelis accurately reproduced, problems are unlikely to happen.
The model was fabricated using tetrahedral element. Although the calculation accuracy of
the tetrahedral element is considered to be not as good as hexahedral element, thefabricated model in the present study was segmentalized so that the element figure isapproximated as hexahedral element. Therefore, inaccurate stress concentration andreaction force due to insufficient element could be avoided.
2. Boundary conditions
The same boundary conditions as the strength test of the 20th Conference of JapaneseSociety of Magnetic Applications in Dentistry were used in the present study. A load up to1000 N was applied at 0.1 mm / sec. The results approximated the actual measurement
were obtained by specifically setting the speed and acceleration. However, there was adifference in the metering rod between actual measurement and the analysis. This isconsidered to be due to the fact that the tip of the metering rod is round in the actual
measurement and flat in the analysis. Further discussion is necessary to understand theinfluence of this difference.
3. Elasto-plastic analysis
Although elasto-plastic analysis is barely used in dentistry, it is widely introduced in theindustrial field and gains credibility. In the present study, a preliminary experiment wasperformed to reconfirm the credibility.
4. Metal treatment
Mechanical properties of the hardening and softening heat treatments were used for
12Wt% Au-Ag-Pt alloy. Although cast strength was measured in the actual measurement,
normalized mechanical properties were applied in the present study. This is due to the factthat cast strength is not consistent, and, therefore it was considered inappropriate to use forsimulation.
5. Analysis result
The graph obtained by the preliminary analysis approximated the actual measurement
graph. The result suggested that validity of the elasto-plastic analysis using
three-dimensional finite element method was confirmed. Since the main experimentintroduced the same condition setting, the validity of the main experiment was also
considered satisfactory. Actual measurement and analysis values did not completely agree.
This was considered to be the influence of displacement in XY axis direction in actualmeasurement.
In the present study, evaluation was performed using stress distribution and loaddisplacement curve.
Stress distribution was evaluated using the von Mises stress. Although the von Mises
stress cannot be used for compression and tension evaluations, it indicates stressconcentration easily. The results showed stress concentration in the upper margin of theextracoronal attachment groove, and stress transmission to the upper and lower margins offoundation. The similar results were obtained in the break test of actual measurement. A
crown and an abutment tooth were assumed for the foundation, and high stressconcentration was expected in the margin line by receiving a stress in an extracoronalmagnetic attachment. The same condition setting as the preliminary experiment wasapplied in the load displacement curve, and the results were compared and discussed withactual measurement of the extracoronal magnetic attachment strength test by Shoji fromthe First Department of Prosthodontics, School of Dentistry, Aichi-Gakuin University. The
actual measurement was performed during casting. The actual elastic limit was 512 N.
This value was in between softening and hardening heat treatment values. The sameresults were reported by Hideo Nakamura, and therefore, the validity of the present
analysis was confirmed. However, a load displacement curve of the softening andhardening heat treatment had multiple curves instead of two. This is considered to be dueto the element influence after segmentation. It is necessary to raise the precision by using
hexahedral element with multiple nodal points and increasing contact points.

Conclusions
The results of the elasto-plastic analysis confirmed that an extracoronal magnetic attachment
has wide elastic area as actual measurements. Analytical values demonstrated that deformation
does not occur until 733 N in the hardening heat treatment, and 390 N in the softening heattreatment.
References
1)

T. Masuda, H. Kumano, Y. Nakamura et al.: Stress Analysis of Extracoronal Magnetic
Attachment using Three-dimensional Finite Element Method, The Journal of the JapaneseSociety of Magnetic Applications in Dentistry, 16 (1): 18 – 22, 2007

2)

H. Nakamura: An Influence of Heat Treatment on Fatigue Strength of Au-Ag-Pd Cast,
Dental Materials Journal, 16 (2) 141 154, 1997