Computer Methods in Biomechanics and Biomedical Engineering, 2015 Vol. 18, No. 14, 1543–1554, http://dx.doi.org/10.1080/10255842.2014.927446

Stress analysis of a complete maxillary denture under various drop impact conditions: a 3D finite element study Emin Sunbuloglu* Faculty of Mechanical Engineering, Istanbul Technical University, Inonu Cad. No: 65, Gumussuyu, Beyoglu, Istanbul 34437, Turkey (Received 11 December 2013; accepted 20 May 2014) Complete maxillary dentures are one of the most economic and easy ways of treatment for edentulous patients and are still widely used. However, their survival rate is slightly above three years. It is presumed that the failure reasons are not only due to normal fatigue but also emerge from damage based on unavoidable improper usage. Failure types other than long-term fatigue, such as over-deforming, also influence the effective life span of dentures. A hypothesis is presumed, stating that the premature/ unexpected failures may be initiated by impact on dentures, which can be related to dropping them on the ground or other effects such as biting crispy food. Thus, the behavior of a complete maxillary denture under impact loading due to drop on a rigid surface was investigated using the finite element method utilizing explicit time integration and a rate-sensitive elastoplastic material model of polymethylmethacrylate (PMMA). Local permanent deformations have been observed along with an emphasis on frenulum region of the denture, regardless of the point of impact. Contact stresses at the tooth–denture base were also investigated. The spread of energy within the structure via wave propagation is seen to play a critical role in this fact. Stress-wave propagation is also seen to be an important factor that decreases the denture’s fatigue life. Keywords: impact simulation; complete maxillary denture; explicit method; finite element analysis; drop impact

Introduction Maxillary complete dentures are an economic and still a widely used method of treatment for edentulous patients. They are used especially where cost is an important issue; the most economical way is most often all polymethylmethacrylate (PMMA) teeth and denture base prostheses. Future predictions of complete denture usage still show an almost increasing or steady requirement of their application, at least for the scope of the next decade (Marcus et al. 1996; Douglass et al. 2002; Smith and McCord 2004; Cooper 2009; Carlsson and Omar 2010; Dog˘an and Go¨kal 2012). The outcomes of studies conducted in the 1990s (Marcus et al. 1996; Douglass et al. 2002) are consistent with the newer outcomes of Cooper (2009), Carlsson and Omar (2010) and Dog˘an and Go¨kal (2012), though they seem to represent focus on different geographical bounds. Dog˘an and Go¨kal (2012) state also consistent results with the US and UK outcomes, saying that edentulism in Turkey is exhibiting similar trends. Thus, it is important to consider that high numbers of PMMA maxillary dentures are yet to be applied worldwide every year. On the economical scale, either from the viewpoint of material requirement, or dentistry and patients 2 point of view, it can be considered that an important focus of interest to conduct research on endurance is essential, which recalls understanding denture behavior under various loading scenarios, material behavior requirements and prediction of zones for improving impact resistance as well as prolonged fatigue life.

*Email: [email protected] q 2014 Taylor & Francis

One of the most common problems in this field of prosthetic dentistry is the fracture of acrylic complete dentures (Khasawneh and Arab 2003; Prombonas and Vlissidis 2006, 2009; Cheng, Cheung, et al. 2010); Cheng, Li, et al. 2010. It is well known that an edentulous patient can only exert occlusal forces at a level of 15 –25% of dentate patients and an acrylic complete denture bears tensile stress values about 48– 62 MPa, and compressive stress values about 75 MPa considering local stress concentrations (Ates et al. 2006). As a consequence, the denture is not expected to fracture under functional masticatory forces (Beyli and von Fraunhofer 1981; Ates et al. 2006). However, fractures in dentures are reported. Due to repeated flexing of the denture base during normal chewing progress (Beyli and von Fraunhofer 1981; Darbar et al. 1996; Khasawneh and Arab 2003), flexural fatigue is said to be the most dominant cause. Additionally, it has been reported by Khasawneh and Arab (2003) that maxillary dentures are observed to exhibit fatigue and need repair more than mandibular dentures. Many methods of experimental stress analysis, such as brittle coating, photoelastic models, strain gauges, have been used to examine the stress distribution in complete maxillary dentures as in Prombonas and Vlissidis (2006, 2009), as well as numerical models applying finite element methods (FEM; Beyli and von Fraunhofer 1981; Darbar et al. 1996; Hengyi et al. 2004; Ates et al. 2006; Prombonas and Vlissidis 2009; Cheng, Li, et al. 2010). All these

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studies show that the stress concentrates in the anterior palatal areas of maxillary dentures. In a finite element analysis (FEA) study, it has been additionally stated that the critical area of peak stress concentration is at the beginning of the palatal aspect of tooth –denture base interface (Darbar et al. 1996). However, all these studies are mainly quasi-static in-vitro studies only considering stress fluctuations at most up to chewing frequencies. In this study, the behavior of maxillary complete dentures under impact loading conditions due to a drop on a rigid floor has been investigated using FE methods. Dynamic simulations utilizing rate-sensitive elastoplastic material models and explicit integration have been utilized, aiming at demonstrating the stress fluctuations and accumulating permanent deformations on the denture due to impact, which is directly related to either comfort of the user due to increasing slackness or decreasing fatigue life of denture due to the high-frequency oscillations of stress due to wave propagation.

Materials and methods A PMMA complete maxillary denture with radio-opaque teeth was prepared to generate a three-dimensional (3D) model based on the real geometry of a random patient of average maxillary size. The model was initially scanned using a 3D Cone-Beam CT for dental applications (NewTom ConeBeam 3D Imaging, AFP Imaging Corporation, New York, NY, USA). The obtained images were processed separately to obtain the geometries for the tooth volumes and (a)

(b)

S1 - On central incisor (d)

(c)

S2 - On buccal flange (e)

S4 - On buccal base side of first molar

Figure 1.

the denture volume separately. Meanwhile, both point clouds were edited to remove topological anomalies due to DICOM image processing such as noisy data and irrelevant holes using point cloud editing software (Polyworks, InnovMetric Software, Inc., Que´bec, Canada). The final point cloud for both the denture base and the 14 teeth volumes were watertight and had smooth curvature continuity. The models were then transferred into CATIA CAD environment (Dassault Syste`mes SA., Ve´lizy-Villacoublay, France), where a surface-fit is performed on the point cloud for each tooth and the denture and the model finally got converted into a solid 15-member assembly model of 14 teeth and a denture. This way of modeling enabled the proper definition of the tooth–denture interface, so that the stress distribution of the interface would also be investigated during the drop simulation. Five scenarios were considered for simulating dropsafety evaluation of the complete maxillary denture. These simulated the drop of the denture on the central incisors (S1), on the denture’s buccal base side (S2), on the first molar tooth (S3), on the buccal denture base side of the first molar tooth (S4) and on the paratuber area of the denture base (S5). The ground was modeled as a rigid surface for all analyses. Each scenario had a different contact surface defined as shown in Figure 1(a) – (e). The naming convention for the teeth while referring within the text is also shown in Figure 1(f). Initial state velocity conditions are common for simulating impact analysis. This way, the analysis time is greatly reduced, as the free fall phase is not considered

S3 - On first molar (f)

S5 - On paratuber area of the denture base

Naming convention of teeth

Drop scenarios for upper denture (a – e) and the tooth naming convention (f).

Computer Methods in Biomechanics and Biomedical Engineering and analyzed. This method is also utilized in this study, and all the initial velocities were applied normally to the contact surface of each scenario to all members of the denture. The reference drop height to calculate the drop velocity was assumed to be 1 m as an approximation to a person standing and missing the denture from hand. Thus, the initial velocity magnitude is taken to be 4.43 m/s for the free calculated using the well-known formula pffiffiffiffiffiffiffifall, ffi V ¼ 2gh, with g ¼ 9:81 m=s2 . Contact surface for each scenario was 1 mm away from the denture initially. Gravitational load toward the contact surface was also applied to the denture. Contact interaction was defined between the rigid surface and the denture. The rigid surface was fixed in space. No other boundary conditions were applied on the denture. The tooth–denture interface for each coupling region is modeled as a rough non-separating contact. Thus, stress transfer in normal to contact and the two principal shear components could be extracted to obtain the most detailed condition for the interface. No separation due to degradation of the interface and/or exceeding the limit values of bonding was assumed in the model: This was considered as a comparison task for post-processing and data evaluation. PMMA density was assumed to be r ¼ 1100kg=m3 . The weight of the denture model measured 14.5 g in FEA environment, which is compatible with the real applications. The elastoplastic strain-rate-dependent material data were derived from mainly Mulliken and Boyce (2006), and visually compared to data in works by Hengyi et al. (2004), Richeton et al. (2006), Varghese and Batra (2009), Arruda and Boyce (2001) and Chen et al. (2002), which are almost similar to the extent of availability of data. The modulus of elasticity is taken as 4.0 GPa based on the approximation that strain rates are high and the modulus exhibit some sort of asymptotic behavior as can be seen from experiments of Mulliken and Boyce (2006). Modulus is not modeled as ratedependent, but the yield stress exhibits rate-dependent behavior as in Mulliken and Boyce (2006). The Poisson’s ratio is assumed to be constant throughout the analysis as 0.3. Material damping was not applied. The pre- and post-processing tasks were carried out on ABAQUS/CAE environment, and the solver was ABAQUS/Explicit with double precision (ABAQUS FEA Package, Dassault Syste`mes Simulia Corp., Ve´lizyVillacoublay, France). Explicit solution technique was preferred to investigate the consequences of initial impact on the denture. 10-Node tetrahedral element type (C3D10M) was used for generating the finite element mesh, to ensure proper representation of the stress distribution even at complex parts of the geometry as well as accurate representation of the contact interface pressure and shear stress components. Each model consisted of 87,032 C3D10M and 9975 rigid surface elements along with 157,107 nodes in total (Figure 2). Throughout the analysis, mass scaling was used to keep the stable time step

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at 3.0E 2 8 s, but the change in mass was less than 3% for the whole model at any stage of the analysis. Data were extracted and recorded at 100-kHz sampling rate (10 ms) intervals. Solver was run on HP DL 585-G7 (48 cores, 256 RAM, 3TB HDD) Server. Total analysis time was chosen to be 2.5 ms for each analysis based on the fact that in a previous pilot study by the author (Sunbuloglu 2013), the extremes of output quantities of interest for evaluation of results were seen to reach their peak values at approximately 1.5 ms after impact. Results All the analyses were evaluated based on the interface stresses at the tooth – denture interface, the global stress localizations and overall plastic deformations of the denture based on the geometric and material model incorporated in the study. Interface stresses The interface stresses between the tooth and the denture were highly transient with both shear (in-local tangent plane) and normal (contact pressure) components existing. Data have been processed for each analysis, and the extreme values of these quantities have been obtained. The data are tabulated in Table 1. It can be seen that both compressive and tensile interface normal stresses exist which may cause cracks and debonding at the tooth – denture interface. The shear stress components were seen to oscillate up to 105 MPa peak-to-peak (Tooth R1-Scenario S1), and tensile interface stresses up to 160.5 MPa could be observed (Tooth R5-Scenario S3). The oscillations of interface stress components occur at frequencies of about 1.5 –2 kHz as the main frequency, similar to observations at frenulum region stresses (Figure 3). Localization of the extreme components is also varying with scenario and with the localization of the hit as it can be seen for contact pressures in Figure 4 and shear components in Figure 5. Stress values observed on denture The denture itself is also prone to highly dynamic stresses. The extreme values of Von Mises stresses extracted are shown in Figure 6. It can be seen that, depending on the position of the hit on ground, the distribution of peak stresses varies, but there are locations that are prone to high stresses independent of the position of the hit: The most explicit of these points are being the lower dip of the frenulum region and the inner lingual vicinity of the incisors. The numerical values of peak Von Mises stress values for selected element centroids (shown in Figure 2) on the model are given in Table 2. Also, the peak Maximum Principal stress values are provided in Table 3 due to its importance in crack initiation. It is also important

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Figure 2.

E. Sunbuloglu

Finite element mesh views of the denture model and IDs of selected elements.

to consider the stress oscillations and peaks observed on the denture near the tooth –denture interfaces, where the denture material is relatively thin and is prone to failure much easily. The numerical values of peak Von Mises stress values and Maximum Principal stress values around the tooth – denture interfaces are given in Tables 4 and 5.

Permanent deformations observed on denture Permanent deformations are not observed on the denture given the available material data, only except for the points of hit for each scenario. The only exception to this outcome is the frenulum region under scenario S2, when the frenulum dip is prone to plastic deformation too

R7

R6

R5

R4

R3

R2

R1

L7

L6

L5

L4

L3

L2

L1

Tooth

Table 1.

Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min

62.7 246.2 29.4 234.5 29.8 231.2 68.1 230.3 25.0 229.8 31.4 233.8 18.7 237.2 79.2 239.8 40.1 231.1 38.4 256.6 35.7 226.0 33.6 228.0 19.8 224.9 12.1 214.8

S1

14.2 240.7 18.2 223.2 9.2 217.6 16.6 248.9 10.2 214.4 19.6 222.7 17.4 230.2 23.0 233.3 19.0 224.8 30.7 223.1 8.5 214.4 5.6 214.5 15.7 216.7 9.6 29.2

S2 79.0 276.1 22.4 226.6 21.8 222.6 43.4 248.6 18.4 241.6 39.6 243.4 40.3 250.4 38.5 268.3 48.2 238.5 46.4 266.1 72.5 298.4 98.4 2160.5 40.5 254.9 22.2 240.9

S3 38.9 239.8 8.4 28.7 9.2 29.3 15.8 217.6 8.6 211.1 14.5 221.1 12.2 214.8 15.6 245.2 37.9 264.0 16.5 240.0 16.4 242.2 13.8 229.8 15.3 238.7 7.1 222.1

S4

Contact pressure (MPa)

14.4 229.4 10.3 215.2 8.2 210.3 14.3 218.8 8.4 29.9 13.7 217.3 10.9 217.9 10.4 227.1 17.0 219.4 12.9 226.2 9.9 215.7 7.6 221.2 17.8 249.5 12.8 252.8

S5

S1 31.3 2 36.7 30.5 2 18.9 9.8 2 11.0 18.9 2 18.3 20.4 2 12.7 13.8 2 15.3 15.0 2 14.2 44.1 2 49.7 30.8 2 25.5 25.8 2 27.5 15.8 2 20.9 19.0 2 18.5 13.8 2 17.5 12.1 28.4

Peak values of interface stresses at each tooth – denture interface.

14.5 2 21.2 9.3 2 13.3 7.9 2 10.6 17.1 2 14.1 9.0 2 13.1 15.1 2 11.9 12.0 2 12.2 29.7 2 17.7 14.6 2 18.4 15.1 28.8 6.0 28.0 8.8 25.1 7.6 2 10.9 6.3 27.6

S2 36.6 2 38.7 39.9 2 20.9 12.9 2 13.4 24.2 2 23.3 25.6 2 17.9 23.5 2 34.0 32.3 2 27.2 32.6 2 35.5 26.1 2 20.1 44.1 2 38.9 27.2 2 27.2 38.7 2 20.3 27.7 2 31.7 24.4 2 24.8

S3 14.8 2 11.4 6.0 2 7.3 7.2 2 8.2 8.2 2 13.2 13.1 2 8.3 9.4 2 8.5 9.2 2 11.6 34.8 2 24.2 45.4 2 17.4 22.2 2 10.2 37.7 2 22.0 23.3 2 11.4 22.6 2 13.7 11.3 2 14.0

S4

Contact shear component 1 (MPa)

12.2 2 12.8 8.6 2 9.4 8.1 2 16.3 12.1 2 13.0 16.0 2 7.5 9.1 2 16.5 10.8 2 10.7 22.4 2 12.3 11.3 2 11.1 12.1 2 11.1 8.4 2 7.4 18.9 2 9.5 12.5 2 9.6 29.7 2 10.7

S5 31.7 2 41.2 13.6 2 15.1 16.9 2 9.4 25.5 2 12.6 18.7 2 24.5 23.0 2 14.8 11.0 2 15.5 27.1 2 78.1 28.8 2 16.8 25.2 2 23.7 30.7 2 16.2 16.2 2 14.1 24.4 2 12.3 13.1 2 9.6

S1 15.4 2 21.1 10.3 2 14.1 9.5 2 9.3 9.6 2 18.2 14.5 2 31.9 8.5 2 10.3 9.6 2 13.4 11.0 2 24.3 9.2 2 13.5 11.7 2 13.7 10.2 2 6.6 4.5 2 5.8 15.8 2 9.2 7.5 2 7.3

S2

25.1 2 27.6 11.7 2 18.6 17.0 2 13.7 17.2 2 20.5 19.3 2 23.4 30.1 2 20.6 18.8 2 24.1 33.1 2 17.7 30.5 2 18.4 27.9 2 47.0 41.7 2 21.2 25.7 2 28.5 27.7 2 25.4 20.1 2 29.1

S3

12.2 2 8.4 7.5 2 4.7 6.5 2 6.1 7.7 2 7.2 19.7 2 9.4 7.2 2 8.5 6.7 2 9.5 20.5 2 16.9 28.8 2 15.5 23.6 2 26.6 14.7 2 17.8 14.9 2 16.5 11.0 2 14.8 7.1 2 14.3

S4

Contact shear component 2 (MPa)

9.7 2 14.8 7.6 2 8.5 9.5 2 9.0 9.3 2 12.9 16.0 2 11.4 10.2 2 11.9 10.2 2 7.4 11.3 2 8.3 9.7 2 8.2 9.0 2 9.7 7.7 2 12.6 12.0 2 7.0 19.8 2 13.3 13.0 2 17.6

S5

Computer Methods in Biomechanics and Biomedical Engineering 1547

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E. Sunbuloglu (a) 180 S1

160

S2 S3

140

S4 120

S5

100 80 60 40 20 0 0.00

0.50

1.00

1.50

2.00

2.50

0.50

1.00

1.50

2.00

2.50

(b) 120 S1 S2 100

S3 S4

80

S5

60

40

20

0 0.00

Figure 3.

Time plot of Von Mises (a) and Maximum Principal (b) stresses at frenulum dip.

(PEEQ ¼ 0.02%). The measure of plastic deformation is taken as the equivalent plastic strain (PEEQ) observed during the analyses. It has been seen that the point of contact for the teeth also exhibits plastic deformations, but it is not directly related to plastic deformation on the denture base.

Discussion Due to cost efficiency, PMMA dentures with PMMA teeth are widely used and are expected to be used in the near future (Cooper 2009; Carlsson and Omar 2010; Dog˘an and Go¨kal 2012). However, it is a well-known fact that complete maxillary dentures suffer from frequent failure due to fracture with a common crack path in the midline

(Prombonas and Vlissidis 2009; Cheng, Cheung, et al. 2010). Similarly, in this study, for all the impact scenarios S1 –S5, the path from frenulum to anterior palatal area is seen to be prone to high stress values that are oscillatory in character. Results of recent experimental (such as those of Prombonas and Vlissidis 2006, 2009) and finite element studies (such as Ates et al. 2006; Cheng, Cheung, et al. 2010; Cheng, Li, et al. 2010) of the denture structure coincide with this point, and it can be stated that reasons causing fracture over this path may not only be related to daily-use forces as greatly discussed in the literature. Moreover, one of the most common undesired but unavoidable loading conditions on the (maxillary) complete dentures are impact loadings, such as accidental drops on a rigid surface from some height. This is a case

Computer Methods in Biomechanics and Biomedical Engineering Distribution of max contact pressure [MPa]

Distribution of min contact pressure [MPa]

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Legend

S1

Compression S2

S3

S4 Tension S5

Figure 4.

Extreme values distribution of contact pressure at the tooth – denture interfaces.

from real life which cannot be easily avoided. To the author’s knowledge, the effect of impact conditions on the acrylic maxillary complete dentures due to a drop on ground has not been considered in investigating their fracture behavior. The only studies on impact-like loading are applied on dentures by a drop-tower test method by Ahmad et al. (1982) and Kim and Watts (2004), which lack the reality of a drop as the dentures are fixed but a mass is dropped onto each. The work by Ahmad et al. (1982) is mainly focusing on fiber reinforcement in the mid-surface and its relative effectiveness. Studies using strain gages or FEM have concentrated on the stress distribution of the maxillary complete

dentures under quasi-static loading conditions. They express results of simulating expected biting forces (such as Prombonas and Vlissidis 2006, 2009 for strain gages and Darbar et al. 1996; Ates et al. 2006; Cheng, Li, et al. 2010 for FEM and references therein) by either using twodimensional (2D) or 3D models of dentures. 2D FEM has been shown to be effective for the treatment of problems of plane stress, and plane strain, but 2D FEM primarily provides information concerning the plane of interest or local variation of a parameter, disregarding the full picture of stress distribution (Ates et al. 2006), unlike 3D FEM analysis despite its requirements for much more dense mesh generation. However, this is not of much importance

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E. Sunbuloglu Distribution of max contact shear [MPa]

Distribution of min contact shear [MPa]

Legend

S1

S2

S3

S4

S5

Figure 5.

Extreme values distribution of contact shear at the tooth – denture interfaces.

with increasing compute power availability. In a recent study (Phunthikaphadr et al. 2009), the effect of transient pressure transfer from tooth to support has also been studied experimentally, but it does not have a full model of the denture to see its behavior completely under such a loading case. The stress data obtained via detailed modeling of the denture –tooth interface in this study can be regarded as providing the dentists much more detailed information on interface stresses. For dentures, it is theoretically assumed that the teeth and the acrylic base are perfectly united. Based on the current model presented, it can be seen that such models may also help choosing the resin type and the

stress limits that the interface resin and/or chemical bonding should be able to safely resist. It has been seen that the tooth –denture interfaces of PMMA dentures with teeth of similar material under drop conditions can be prone to tensile stresses up to 160 MPa as an extreme in case of drop S3. The average stress range mostly remains between 80 MPa compression and 65 MPa tension range (Table 1). The shear components are observed to remain in ^ 50 MPa range. In various studies, it is indicated that the debonding stresses at the tooth – denture interface are at the orders of 10– 40 MPa in quasi-static environment in shear (in contact local tangent plane) (Thean et al. 1996; Thean et al. 1998; Mian et al. 2013), and 27– 69 MPa in tensile

Computer Methods in Biomechanics and Biomedical Engineering Distribution of Peak Von Mises stresses on denture [MPa]

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Legend

S1

Stress [MPa]

S2

S3

S4

S5

Figure 6.

Peak values distribution of contact Von Mises stress values on denture.

(normal to interface) directions (Amin 2002; Alsiyabi et al. 2004; Amarnath et al. 2011). These values indicated are much lower than the ones calculated here; however, it should be noted that the tests referenced therein are conducted in quasi-static conditions: Under such conditions, PMMA is much softer and yields more easily compared with its high-strain-rate behavior. On the other hand, the outcomes of a recent FE study about shear tests by Braga et al. (2010) indicate that the testing method also imposes some notch effect on the stress distribution, which may imply that the real failure stresses can be in fact much higher in real tooth – denture interfaces. Notch factors

decreasing apparent strength of conventional strength tests may go up to 4– 6 according to data in Braga et al. (2010), which may also shift the actual interface failure stress values up to 150 –200 MPa. In the future, studies related to compare these values with those of the daily-use data that cause cyclic loading to failure will provide more insight to the fatigue phenomenon of denture structures. The fatigueoriented approach is expected to help understanding denture fractures in a more systematic way, other than only static stress distribution considerations. The tools to be used then should also include high-frequency high-stress oscillations due to impact-like loading and stress-wave

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Table 2. Peak values of Von Mises stresses at selected locations (element centroids) on denture.

Table 4. Peak values of Von Mises stresses on denture near the tooth interface.

Von Mises stress (MPa)

Von Mises stress (Mpa)

Elem. No. 9938 11169 23994 26455 26573 26759 27277 37384 45887 46151

S1

S2

S3

S4

S5

19.5 88.2 35.6 45.4 54.3 26.3 66.3 44.5 23.1 15.4

5.2 168.1 26.4 8.2 12.6 9.8 24.2 35.1 10.4 7.1

29.2 99.5 40.6 16.5 24.7 40.5 28.4 66.7 46.1 15.3

14.2 85.3 59.5 25.4 31.9 11.3 14.1 22.4 18.0 5.5

11.8 38.9 10.5 6.5 9.8 5.2 11.4 16.5 28.5 14.9

propagation. The example presented in this paper is due to impact; however, biting brittle food (such as hard candies, beer nuts, etc.) will also lead to impact-like stress-wave propagation in the denture due to instant release of load. Although as shown in Ates et al. (2006) that the point of contact at the molar teeth may alter the stress distributions and respective amplitudes of cyclic loading, the concentration of stresses at well-defined regions (especially near the frenulum and the regions near the tooth – denture interfaces of incisors which lie about the lateral symmetry axis of the denture) under various impact conditions as observed in this study may also be helpful in determining the reasons that may lead to fracture of the denture base so that design and/or material improvements can be conducted. It can also be discussed that PMMA brands with superior impact resistance in the market may be safe against fracture due to more sound ductile behavior (in, for example, Lalande et al. (2006), elongation at failure is found to be about 90% for rubber-toughened PMMA) despite the fact that permanent geometric deformations become more evident. It had been found in a previous study by Smith and McCord (2004) that slackness is one of the major complaints of dentures which can also be developed by permanent deformations due to impact. It

Tooth L1 L2 L3 L4 L5 L6 L7 R1 R2 R3 R4 R5 R6 R7

Elem. No. 9938 11169 23994 26455 26573 26759 27277 37384 45887 46151

S1

S2

S3

S4

S5

20.1 84.9 39.6 18.4 14.9 30.7 20.7 47.9 22.3 15.6

5.3 40.7 14.8 7.0 12.4 9.5 26.7 24.2 7.6 5.0

30.1 98.5 44.7 8.1 19.2 46.4 27.6 71.2 29.2 14.3

4.3 27.4 11.8 21.2 32.5 10.7 15.0 17.3 18.1 5.6

10.9 40.6 11.6 5.9 10.0 3.8 9.4 17.2 29.0 14.9

S2

S3

S4

S5

90.2 40.4 34.9 42.6 50.4 35.8 25.3 103.5 48.3 57.0 46.6 39.2 33.7 22.6

44.9 27.0 26.4 27.9 67.2 23.6 22.6 56.2 29.1 37.3 21.1 11.5 19.5 12.1

74.7 53.0 27.7 35.6 56.9 44.6 48.4 55.4 61.2 56.8 67.4 66.9 53.5 49.7

33.8 13.3 12.1 17.5 51.7 18.9 21.4 51.3 53.2 42.1 75.1 38.7 34.6 20.8

33.0 20.0 19.6 19.9 43.0 20.6 18.6 21.4 17.1 19.9 19.3 21.5 45.7 64.9

can further be stated that the high-strain-rate yielding stress of dental PMMA should be improved along with fatigue limit of the material: Wave propagation in PMMA denture results in high-frequency stress oscillations which decrease the fatigue life, a phenomenon which can also be observed in the case of biting harder and crispy food. Combining these facts together yields an optimization problem on selection of material properties for denture applications. To figure out this fact, exact material data of such dental resins should be made available for brands, which can be a further field of study. Mechanical properties of various dental acrylic types under controlled laboratory conditions are widely available (Phunthikaphadr et al. 2009; Cheng, Li, et al. 2010) stating that various properties should exist for a good-quality one without their relevance to the real-life loading conditions and geometrical models being invesTable 5. Peak values of Maximum Principal stresses on denture near the tooth interface. Maximum Principal stress (MPa) Tooth

Table 3. Peak values of Maximum Principal stresses at selected locations (element centroids) on denture.

S1

L1 L2 L3 L4 L5 L6 L7 R1 R2 R3 R4 R5 R6 R7

S1

S2

S3

S4

S5

57.4 37.5 40.3 50.2 43.6 31.7 23.1 40.5 40.8 63.4 50.0 45.7 39.6 25.8

58.4 30.0 26.9 25.1 53.8 29.0 27.3 40.7 29.4 23.7 20.0 10.9 23.8 12.1

87.0 38.9 28.6 44.3 39.8 53.6 53.2 55.3 56.8 49.5 56.3 63.0 48.7 60.4

43.0 13.9 12.0 17.9 34.2 21.2 25.2 49.6 51.9 50.7 86.2 40.1 39.8 21.8

36.4 20.6 17.2 20.0 36.3 26.1 21.2 21.8 20.1 20.1 18.0 23.6 49.2 63.9

Computer Methods in Biomechanics and Biomedical Engineering tigated in detail. However, the stress – strain relationship of PMMA, either intact or rubber-toughened, is highly rate and temperature dependent in terms of yield stress and plastic flow behavior. Thus, it requires more than scalar lists of impact toughness values for proper application of FEM models and/or experimental stress analysis techniques to understand mechanical response of PMMA structures to external loading. However, almost no data are available, especially on the commercially available brands of dental PMMA in terms of rate-dependent stress – strain behavior. Assuming that the general behavior of PMMA as a material is mostly similar in dental and other applications and seeking through specific papers on viscoelastoplastic constitutive modeling studies (such as in works by Mulliken and Boyce 2006; Richeton et al. 2006, 2007 or similar), good approximations to its rate dependency in terms of yield stress and stress –strain behavior can be incorporated into FE models. Once going through the data readily available therein, it can be seen that both in the quasi-static conditions and the high-strain-rate conditions, the effect of rate dependency is highly profound. In a previous preliminary study by the author (Sunbuloglu 2013), dissipation due to inelastic deformations is seen to be maximum for drop on the denture’s labial base margin (S2), indicating that this is a critical case to consider for denture failure. However, the material model used there did not include data for high strain-rate behavior of PMMA above 10 s21. The difference among results presented there and here also points out the importance of high-quality material data to be available to obtain accurate results in numerical studies. The present study incorporates advanced data of PMMA (though not explicitly dental), and it is seen that the plastic deformations are thus very limited to the regions near the area of contact, except for one case (S2) where the frenulum dip is exhibiting permanent strains. This is based on the fact that yield stress is assumed to increase about four-fold as the strain rates increase to 1000 s21. The material model considered in this study results in highfrequency oscillations of elastic stress at a point which is expected to be far higher than the infinite-life fatigue limit for PMMA. An example of such oscillations of stress at the frenulum dip is given in Figure 3 for all five scenarios. The analysis of reinforced denture structures under impact conditions can also be regarded as an interesting topic to the extent that the anisotropic rate-sensitive elastoplastic behavior of the composite structure can be extracted experimentally in a useful manner for FEM usage. Experimental studies have shown evidences of improvement in mechanical properties of such reinforcements under impact conditions (Kim and Watts 2004). Models incorporating different materials (such as complete porcelain teeth, veneer coverings, etc.) with detailed interface modeling, similar to the way presented in this study, are also expected to yield valuable information.

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Investigation of the multi-material complex interface structure may also help developing more robust denture bases. The outcomes of systematic research on various material couples and interface conditions will be valuable both for the dentists who want to apply available materials in the clinic in a more durable, comfortable and useful fashion for people in need of dentures, and for the chemical engineers who strive to develop proper adhesives and sophisticated tooth, covering and base materials that will enable more robust integrity. Conclusions Yield stress, flow properties and fatigue behavior of PMMA used while forming a complete maxillary denture are important aspects increasing the useful life of the denture not only due to daily use, but also regarding undesired real-life actions that occur. Impact toughness of PMMA should serve to improve also these measures, other than only elongation-to-rupture. Severe permanent deformations of the denture observed might cause also discomfort to patients. Plastic deformations, which have been observed at regions other than the point of contact, are limited to frenulum region based on the current material model used, and it coincides with real-world crack initiation locations and failure paths. Propagation of energy is a critical phenomenon for impact-like loading conditions that cause stress-wave propagation and highfrequency alternating stresses on the denture, which decreases fatigue life just within a few milliseconds. It has been concluded to be important to consider the accidental occurrences during evaluation of failure of dentures as well as the loading scenarios for intended use during developing more ergonomic and long-useful-life denture geometries. Better designs can be developed once (a) ratedependent constitutive behavior and (b) fatigue-life-curves proper for engineering analysis of commercially available dental PMMA types are made available. The need for high-quality material data of dental PMMA for numerical applications is seen to be crucial, and importance of evaluating tooth – denture interface stresses is seen to provide a new scope to denture production. Evaluation of different material and interface combinations for teeth and denture base materials is also envisaged as a further field of study, the outcomes of which are to provide the detailed insight for both the dentists in clinic and the engineers developing dental materials. Acknowledgements The author expresses his special thanks to Dr Altug Cilingir, DDS PhD, and Dr Hakan Bilhan, DDS PhD, for their assistance during the preparation of this study, and Dr Ergun Bozdag, Mech. Eng. PhD for his encouragement and kind help. Support to the Biomechanics Laboratory, Istanbul Technical University, Faculty of Mechanical Engineering from State Planning Organiz-

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ation via Project DPT-2003K120630/90191 is kindly acknowledged. The author would also express special thanks to Teknodent Radiological Imaging Center –Istanbul for its kind support and advice during the scanning and model generation of the denture models.

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