Finite element stress analysis of restored teeth

Influence of "MOTRCS" factors on the performance of various direct and indirect restorations: A finite element analysis

Aim of the Study:

The purpose of the study is to evaluate the occlusal relationship of the mesiobuccal cusp of a mandibular first molar with the marginal ridge of maxillary first molar and second premolar and to analyze the effect of the above occlusal relation on different direct and indirect restorations using finite element analysis (FEA).

Methodology:

Four hundred volunteers studying in a dental college were screened, of which 100 volunteers were selected for studying occlusal relationships based on the inclusion and exclusion criteria. The two most common occlusal relationships were considered for analyzing two direct (amalgam and direct composite restorations) and two indirect restorations (composite and ceramic restorations). Three-dimensional (3D) scanning of the models was performed, and Class II tooth preparations specific for each restorative material were prepared digitally on 3D models. FEA was employed to study von Mises (VM) stress, principal stresses, and cuspal deflection for each restorative material, and failure of the tooth-restoration unit was calculated using the modified Mohr failure criterion.

Results:

Among all the analyzed materials, cuspal deformation, principal stresses, and VM stresses were high for direct composite restoration and least for ceramic inlay. According to modified Mohr criteria, except for direct composite, all other materials performed better.

Conclusion:

Silver amalgam and ceramic restorations presented with minimal stress concentration and cuspal deflection, and Type I occlusal relationship presented with higher stress concentration compared to Type II.

Effect of Shrinking and No Shrinking Dentine and Enamel Replacing Materials in Posterior Restoration: A 3D-FEA Study

The aim of the present study was to investigate the effect of shrinking and no shrinking dental filling materials combination in posterior restorations under the combined effects of polymerization shrinkage and occlusal load by means of 3D Finite Elements Analysis. Six computer-generated and restored class I or class II cavities models of a lower molar were designed in the CAD software and evaluated according to the cavity and restorative procedure. Different shrinking and no shrinking adhesive materials combination with diverse Young’s modulus were considered. A food bolus was modeled on the occlusal surface replicating the chewing load using static linear analyses Polymerization shrinkage was simulated for the shrinking different restorative materials. The maximum principal stress was selected as analysis criteria. All models exhibited higher stresses along the dentine restoration interfaces with different magnitude and a similar stress trend along enamel restoration interface. Stress values up to 22 MPa and 19 MPa were recorded in the enamel and restoration, respectively. The use of elastic not shrinking material layer in combination with bulk fill composite reduced the stress magnitude in dentine and enamel to replace dental tissues. Class I and class II posterior cavities adhesively restored with shrinking filling material’s combination showed the most unfavorable stress concentrations and the multilayer technique is a promising restorative alternative in posterior adhesive restorations when deep dentin and enamel volumes are missing.

The use of different adhesive filling material and mass combinations to restore class II cavities under loading and shrinkage effects: a 3D-FEA

3D tooth models were virtually restored: flowable composite resin + bulk-fill composite (A), glass ionomer cement + bulk-fill composite (B) or adhesive + bulk-fill composite (C). Polymerization shrinkage and masticatory loads were simulated. All models exhibited the highest stress concentration at the enamel-restoration interfaces. A and C showed similar pattern with lower magnitude in A in comparison to C. B showed lower stress in dentine and C the highest cusps displacement. The use of glass ionomer cement or flowable composite resin in combination with a bulk-fill composite improved the biomechanical behavior of deep class II MO cavities.

A 3D finite element analysis of stress distribution on different thicknesses of mineral trioxide aggregate applied on various sizes of pulp perforation

OBJECTIVES

The aim of this study was to evaluate the stress distribution on different thicknesses of mineral trioxide aggregate (MTA) placed on various widths of pulp perforations during the condensation of the composite resin material.

MATERIALS AND METHODS

The mandibular molar tooth was modeled by COSMOSWorks program (SolidWorks, Waltham, MA). Three finite elemental analysis models representing 3 different dimensions of pulp perforations, 1, 2, and 3 mm in diameter, were created. The perforation area was assumed as filled with MTA with different thicknesses, 1, 2, and 3 mm for each pulp perforation width, creating a total of 9 different models. Then, a composite resin material was layered on MTA for each model. A 66.7 N load was applied and an engineering simulation program (ANSYS, Canonsburg, US) was used for the analysis. Results were presented considering von Mises stress criteria.

RESULTS

As MTA thickness increased, the stress values recorded within the area between pulp and MTA decreased. Strain was decreased when the thickness of MTA increased.

CONCLUSIONS

Stresses at MTA-pulp interface and strain on MTA decreased with the increase in MTA thickness.

CLINICAL RELEVANCE

In clinical practice, when MTA is required for pulp capping, using a thick layer of the material seems to be a better option in order to reduce the stress under forces of hand condensation of overlying restorative materials.

Adhesive class I restorations in sound molar teeth incorporating combined resin-composite and glass ionomer materials: CAD-FE modeling and analysis

OBJECTIVES

To investigate the influence of different resin composite and glass ionomer cement material combinations in a "bi-layer" versus a "single-layer" adhesive technique for class I cavity restorations in molars using numerical finite element analysis (FEA).

MATERIALS AND METHODS

Three virtual restored lower molar models with class I cavities 4mm deep were created from a sound molar CAD model. A combination of an adhesive and flowable composite with bulk fill composite (model A), of a glass ionomer cement with bulk fill composite (model B) and of an adhesive with bulk fill composite (model C), were considered. Starting from CAD models, 3D-finite element (FE) models were created and analyzed. Solid food was modeled on the occlusal surface and slide-type contact elements were used between tooth surface and food. Polymerization shrinkage was simulated for the composite materials. Physiological masticatory loads were applied to these systems combined with shrinkage. Static linear analyses were carried out. The maximum normal stress criterion was adopted as a measure of potential damage.

RESULTS

All models exhibited high stresses principally located along the tooth tissues-restoration interfaces. All models showed a similar stress trend along enamel-restoration interface, where stresses up to 22MPa and 19MPa was recorded in the enamel and restoration, respectively. A and C models showed a similar stress trend along the dentin-restoration interface with a lower stress level in model A, where stresses up to 11.5MPa and 7.5MPa were recorded in the dentin and restoration, respectively, whereas stresses of 17MPa and 9MPa were detected for model C. In contrast to A and C models, the model B showed a reduced stress level in dentin, in the lower restoration layer and no stress on the cavity floor.

SIGNIFICANCE

FE analysis supported the positive effect of a "bi-layer" restorative technique in a 4mm deep class I cavities in lower molars versus "single-layer" bulk fill composite technique.

CAD-FE modeling and analysis of class II restorations incorporating resin-composite, glass ionomer and glass ceramic materials

OBJECTIVES

To investigate the influence of specific resin-composite, glass ceramic and glass ionomer cement (GIC) material combinations in a "multi-layer" technique to replace enamel and dentin in class II mesio-occlusal-distal (MOD) dental restorations using 3D-Finite Element Analysis (FEA).

METHODS

Four 3D-FE models (A-D) of teeth, adhesively restored with different filling materials, were created and analyzed in comparison with a 3D model (E) of a sound lower molar. Models A, B & C had "multilayer" constructions, consisting of three layers: adhesive, dentin replacement and enamel replacement. Model A: had a low modulus (8GPa) composite replacing dentin and a higher modulus (12GPa) composite replacing enamel. Model B: had a GI cement replacing dentin and a higher modulus (12GPa) composite replacing enamel. Model C: had a low modulus (8GPa) composite replacing dentin and a very high modulus (70GPa) inlay replacing enamel. Model D: had a lithium disilicate inlay replacing both dentin and enamel with a luting cement base-layer. Polymerization shrinkage effects were simulated and a load of 600N was applied. All the materials were assumed to behave elastically throughout the entire deformation.

RESULTS

Model A showed the highest stress distribution along all the adhesive interfaces of the shrinking resin-based materials with a critical condition and failure risk marginally and internally. Model D, by contrast, showed a more favorable performance than either of the multilayer groups (A-C). Stress and displacement plots showed an elastic response similar to that obtained for the sound tooth model. Model B and Model C performed according to their bilayer material properties. The use of a non-shrink dentin component simulating a GIC clearly affected the shrinkage stress at the basis of the Model B; while the bulk resin composite having a 12GPa Young's modulus and linear polymerization shrinkage of 1% strongly influenced the biomechanical response in the bucco-lingual direction.

SIGNIFICANCE

Direct resin-based composite materials applied in multilayer techniques to large class II cavities, with or without shrinking dentin layers, produced adverse FEA stress distributions and displacements. An indirect lithium disilicate inlay used to replace lost dentin and enamel in posterior restored teeth generated lower stress levels, within the limits of the elastic FEA model.

Fractographical Analysis and Biomechanical Considerations of a Tooth Restored With Intracanal Fiber Post: Report of the Fracture and Importance of the Fiber Arrangements

OBJECTIVE

This article aims to present a fractographic analysis of an anterior tooth restored with a glass fiber post with parallel fiber arrangement, taking into account force vectors, finite element analysis, and scanning electron microscopy (SEM).

METHODS

A patient presented at the Faculty of Dentistry (Federal University of Santa Maria, Brazil) with an endodontically treated tooth (ETT), a lateral incisor that had a restorable fracture. The treatment was performed, and the fractured piece was analyzed using stereomicroscopy, SEM, and finite element analysis.

RESULTS

The absence of remaining coronal tooth structure might have been the main factor for the clinical failure. We observed different stresses actuating in an ETT restored with a fiber post as well as their relationship with the ultimate fracture. Tensile, compression, and shear stresses presented at different levels inside the restored tooth. Tensile and compressive stresses acted together and were at a maximum in the outer portions and a minimum in the inner portions. In contrast, shear stresses acted concomitantly with tensile and compressive stresses. Shear was higher in the inner portions (center of the post), and lower in the outer portions. This was confirmed by finite element analysis. The SEM analysis showed tensile and compression areas in the fiber post (exposed fibers=tensile areas=lingual surface; nonexposed fibers=compression areas=buccal surface) and shear areas inside the post (scallops and hackle lines). Stereomicroscopic analysis showed brown stains in the crown/root interface, indicating the presence of microleakage (tensile area=lingual surface).

CONCLUSION

We concluded that glass fiber posts with parallel fibers (0°), when restoring anterior teeth, present a greater fracture potential by shear stress because parallel fibers are not mechanically resistant to support oblique occlusal loads. Factors such as the presence of remaining coronal tooth structure and occlusal stability assist in the biomechanical equilibrium of stresses that act upon anterior teeth.

Modeling of damage driven fracture failure of fiber post-restored teeth

Mechanical failure of biomaterials, which can be initiated by either violent force, or progressive stress fatigue, is a serious issue. Great efforts have been made to improve the mechanical performances of dental restorations. Virtual simulation is a promising approach for biomechanical investigations, which presents significant advantages in improving efficiency than traditional in vivo/in vitro studies. Over the past few decades, a number of virtual studies have been conducted to investigate the biomechanical issues concerning dental biomaterials, but only with limited incorporation of brittle failure phenomena. Motivated by the contradictory findings between several finite element analyses and common clinical observations on the fracture resistance of post-restored teeth, this study aimed to provide an approach using numerical simulations for investigating the fracture failure process through a non-linear fracture mechanics model. The ability of this approach to predict fracture initiation and propagation in a complex biomechanical status based on the intrinsic material properties was investigated. Results of the virtual simulations matched the findings of experimental tests, in terms of the ultimate fracture failure strengths and predictive areas under risk of clinical failure. This study revealed that the failure of dental post-restored restorations is a typical damage-driven continuum-to-discrete process. This approach is anticipated to have ramifications not only for modeling fracture events, but also for the design and optimization of the mechanical properties of biomaterials for specific clinically determined requirements.

Evaluation of the stress distribution in CFR-PEEK dental implants by the three-dimensional finite element method

CFR-PEEK (carbon fiber reforced-poly ether ether ketone) has been demonstrated to be excellent substitute titanium in orthopedic applications and can be manufactured with many physical, mechanical, and surface properties, in several shapes. The aim of this study was to compare, using the three-dimensional finite element method, the stress distribution in the peri-implant support bone of distinct models composed of PEEK components and implants reinforced with 30% carbon fiber (30% CFR-PEEK) or titanium. In simulations with a perfect bonding between the bone and the implant, the 30% CFR-PEEK presented higher stress concentration in the implant neck and the adjacent bone, due to the decreased stiffness and higher deformation in relation to the titanium. However, 30% CFR-PEEK implants and components did not exhibit any advantages in relation to the stress distribution compared to the titanium implants and components.

Biomechanical Stress Analysis of Mandibular First Permanent Molar; Restored with Amalgam and Composite Resin: A Computerized Finite Element Study

Normal mastication with its varying magnitude and direction generates considerable reactionary stresses in teeth and their supporting tissues. The structure of the human tooth and its supporting tissues is a complex assemblage of materials of varied mechanical properties. The finite element method (FEM), a modern technique of numerical stress analysis, has the great advantage of being applicable to solids of irregular geometry and heterogeneous material properties and therefore ideally suited to the examination of structural behavior of teeth. The mandibular first permanent molar is one of the earliest permanent teeth to erupt in the oral cavity and hence most prone to caries. The purpose of the present study was to construct a two-dimensional FE model of the mandibular first permanent molar and its supporting structures, using a FE software called NISA II-Display III, EMRC, USA to study the following:

• To compare stress distributions patterns when a modeled Class I Cavity was restored with dental amalgam and composite resin.

• To compare the stress distributions pattern when the load was applied to different to locations, i.e.: At the mesial cusp tip, and at the center of the occlusal surface.

Both amalgam and composite resin showed similar stress distribution pattern, however, the magnitudes of stresses generated in the tooth restored with composite resin were higher. Thus, amalgam is a better restorative material in distributing stresses.

Finite element analysis of a new customized composite post system for endodontically treated teeth

This paper investigated the mechanical behavior of a new customized post system built up with a composite framework presently utilized for crowns, bridges, veneers and inlay/onlay dental restorations. The material has been shaped so to follow perfectly the profile of the root canal in order to take advantage of the better mechanical properties of composites with respect to metallic alloys commonly used for cast posts. The analysis has been carried out with 3D finite element models previously validated on the basis of experimental work. The new post system has been compared to a variety of restorations using either prefabricated or cast posts. The structural efficiency of the new restoration has been evaluated for an upper incisor under different loading conditions (mastication, bruxism, impact). Results prove that maximum stress values in restored teeth are rather insensitive to post types and materials. However, the new customized composite restoration allows to reduce significantly the stresses inside the dentinal regions where conservative clinical interventions are not possible.

Finite element analysis of stresses in molars during clenching and mastication

STATEMENT OF PROBLEM

During physiological functions of the masticatory system such as swallowing and chewing, teeth are subjected to variations in force application. Most in vitro analyses of stress have not analyzed the combined forces acting on teeth.

PURPOSE

The purpose of this study was to analyze the stresses induced in a mandibular molar during clenching and chewing of morsels with various elastic moduli.

MATERIALS AND METHODS

The investigation was performed by means of finite element analysis with the use of contact elements. Two-dimensional models of the mandibular first molar and the crown of the opposing maxillary molar were created. The computerized simulation evaluated the clenching and chewing of 4 morsels with different elastic moduli (similar to hard gum, tough meat, bone, and combination of hard gum and bone). The movement of the studied teeth was simulated in the frontal plane. Teeth models crushed morsels and closed into the maximal intercuspation position. The values of stresses in the mandibular molar were calculated during these situations.

RESULTS

The study revealed that clenching of molars and chewing morsels of high elastic moduli resulted in maximal equivalent stresses within occlusal enamel. During mastication of morsels of low elastic moduli the stress concentration was located in the cervical region of the lingual side of the mandibular molar. Masticating a low-elasticity morsel containing a fragment of bone caused the highest equivalent stresses in the lingual wall and high tensile stresses in enamel near the central intercuspal fissure of the tooth studied.

CONCLUSION

During mastication of various morsels, maximal equivalent stresses occurred in occlusal enamel and in the cervical region of the lingual wall of the first mandibular molar. The more unfavorable and highest stresses were exerted during mastication of nonhomogeneous morsels.

Evaluation of two post core systems using two different methods (fracture strength test and a finite elemental stress analysis)

The aim of this study was to compare a fiber composite laminate (FCL) post core and a conventional cast post core system by using two different methods. The first method was a conventional fracture strength test, and the second was a finite elemental stress-analysis method (FEM). For the conventional fracture strength test, 20 extracted, human upper, central incisors were used. The teeth were decoronated, treated endodontically, and restored with two post core systems. After embedding the samples in resin blocks, a loading force was applied to the teeth at a crosshead speed of 5 mm/ min at an angle of 45 degrees to the long axis of the tooth. The data were recorded, and the results were compared by using the Mann-Whitney U test. There was no statistically significant difference between the two post systems (p > 0.05). For FEM analysis, a pseudo three-dimensional model of a maxillary central incisor, theoretically restored with either a cast post or an FCL, was used. The analysis was performed by using the structural analysis program (SAP90). FEM analysis showed that stress was accumulated within the cast post core system, and transmission of stress to supportive structures and the tooth was low. This is an advantage for tooth and supporting tissues. When the FCL post core system was evaluated by FEM, the results indicated that this system transferred stress to supportive structures and the tooth while stress accumulation within the post system was low. This is an advantage for the restoration but disadvantage for the supporting tissues.

Finite element analysis of a glass fibre reinforced composite endodontic post

In this work the mechanical response to external applied loads of a new glass fibre reinforced endodontic post is simulated by finite element (FE) analysis of a bidimensional model. The new post has a cylindrical shape with a smooth conical end in order to adequately fit the root cavity, and to avoid edges that could act as undesired stress concentrators. Mechanical data obtained by three-point bending tests on some prototypes fabricated in the laboratory are presented and used in the FE model. Under various loading conditions, the resulting stress component fields are hence compared with those obtained in the case of two commercial endodontic posts (i.e. a cast metal post and a carbon fibre post) and with the response of a natural tooth. The gold cast post-and-core produces the greatest stress concentration at the post-dentin interface. On the other hand, fibre-reinforced composite posts do present quite high stresses in the cervical region due to their flexibility and also to the presence of a less stiff core material. The glass fibre composite shows the lowest peak stresses inside the root because its stiffness is much similar to dentin. Except for the force concentration at the cervical margin, the glass fibre composite post induces a stress field quite similar to that of the natural tooth.

The effect of stiffness on the localization of tensile stress at the surface of bonded posterior restorations

OBJECTIVES

The aim of this study is to assess the distribution of tensile stress under the conditions representative of tooth-food contact in a restored posterior tooth. The ideal stiffness for a bonded restoration will be predicted.

METHODS

A two-dimensional plane-strain finite element representation of a restored first maxillary molar is created. The restoration with Class I/II bucco-lingual geometry is assigned a range of Young's moduli (E = 10-80 GPa), representative of the range of materials available. In addition, a hypothetical multi-phase model, in which stiffness is gradually increased from the intercuspal concavity to the adjacent enamel, is also created. A food particle is modeled and pushed close to the interface onto the site of (1) intact enamel and (2) restored surface.

RESULTS

For all single-phase models tested, the magnitude of tensile stress at the surface is far greater than that present elsewhere in the tooth. However, the exact position and magnitude of the maximum tensile stress varied according to the modulus assigned to the restoration and the position of load. The results of the model imply that interfacial problems are likely in low-modulus restorations (E = 10-20 GPa), whereas stress-related problems could occur in the intercuspal concavity of high-modulus restorations (E = 40-80 GPa). Of all the single-phase models, tensile stresses are lowest when the Young's modulus assigned to the restoration is 30 GPa. These tensile stresses are reduced in the multi-phase model.

SIGNIFICANCE

Given the limitations of the model, the results indicate that the most suitable modulus for a single-phase posterior bonded restoration is around 30 GPa. Such a modulus is approached in compact-filled composites. In addition, the highly desirable dissipation of load in the multi-phase model should warrant further investigation. It is suggested that the use of an incremental filling technique with region-specific proportions of hard-filler could be one way forward.

The effects of enamel anisotropy on the distribution of stress in a tooth

Enamel is thought to have highly anisotropic stiffness characteristics, because of its prismatic structure. It is probable that the enamel is stiffer in the prism direction compared with a direction perpendicular to it. The prisms are thought to run approximately perpendicular to the enamel-dentin junction. The curvilinear anisotropy that will result can readily be modeled by TOMECH, a finite element program developed at the University of Sheffield, since curvilinearity of mechanical properties is available as an automated feature of this program. The patterns of stress due to an external load were investigated in two-dimensional abstract models, and in a model of a mandibular second premolar, for both anisotropic and isotropic enamel. Results were compared with the commercial code ANSYS and good agreement obtained. Enamel with anisotropic properties was found to have a profoundly different stress distribution under load when compared with models with isotropic enamel. For isotropic enamel, the load path is directed through the stiff enamel shell, while for anisotropic enamel, the load path is directed into the dentin, as the load path follows the stiff direction of the enamel prisms. Thus, if enamel is indeed anisotropic, its function differs greatly from that suggested in previous hypotheses. Enamel with anisotropic material characteristics would provide a hard-wearing protective surface-coating while simultaneously diverting the load away from this brittle, low-tensile-strength phase, thus reducing the potential for tooth fracture.

Effects of posts on dentin stress distribution in pulpless teeth

A finite element analysis was carried out to study the roles of posts in reducing dentin stress in pulpless teeth. Two-dimensional plane strain models of the midlabiolingual section of a human maxillary central incisor were first analyzed. The results showed that the gold alloy post reduced maximal dentin stress by as much as 30%. However, the integrity of the dentin was compromised and the effects of the post were likely to be exaggerated in such models. In an effort to correct for these problems, plane stress models with side plates and axisymmetric models were analyzed. Posts were found to reduce maximal dentin stress by only 3% to 8% when the teeth were subjected to masticatory and traumatic loadings in these latter models. Although posts reduced maximal dentin stress by as much as 20% when the teeth were loaded vertically, teeth such as incisors and canines normally are not subjected to vertical loadings. Thus the reinforcement effects of posts seem to be doubtful in these teeth.

Effect of cavity depth on stresses in a restored tooth

Restorative procedures commonly replace lost tooth structure, but redistribution of functional stresses after treatment is not fully understood. Many restorative methods are dictated by the integrity of the remaining tooth structure, because sparse tooth structure can lead to fracture. It is essential to prevent fractures by having a clear concept of the designs for cavity preparations, and to anticipate the stresses of mastication on the remaining tooth structure. Knowledge of various internal parameters of cavity designs would facilitate selection of the appropriate cavity preparation for a specific clinical situation. Three cavity designs and restorations were examined in this study for stresses using the finite element technique. After placement of restorative materials, the dentin experienced a dramatic change in stress gradient immediately below the pulpal wall, and this response was magnified in deeper cavity preparations. Enamel also exhibited major alterations in the stress gradient in all three designs of cavity preparations. The combination of the changes can cause cracks in the remaining tooth structure, leading to cusp fracture immediately adjacent to the deepest portion of the cavity.

Clinical implications of the response of enamel and dentin to masticatory loads

The success of restorative procedures is dependent on comprehension of the responses of enamel and dentin, including responses to masticatory forces. The regional variation resulting from masticatory forces is critical because clinically it relates to the thickness of enamel and dentin occlusogingivally. Three-dimensional finite element models of an intact mandibular molar were developed to analyze stresses in enamel and dentin occlusogingivally, buccolingually, and mesiodistally. There were dramatic regional variations in the magnitude and character of different stresses caused by masticatory forces, and despite being organically "bonded," enamel and dentin responded independently. This unique behavior with regional variations of these tissues could have serious clinical implications during restorative procedures.

A critique of bond strength measurements

The lack of consistent values for dentine bond strengths in shear or in tension from what are superficially identical experimental procedures has led to ambiguities in the interpretation of the data. These variations in bond strength are usually considered to be related to different adhesive procedures. However so far little attention has been paid to the detail of the test procedures used. In this study the sensitivity of bond strengths to changes in testing conditions has been calculated using finite element stress analysis. It is shown that tensile and shear bond strengths are highly dependent on the geometry of the test arrangement and the materials involved. It is concluded that the concept of 'average stress' for the measurement of bond strength does not stand up to close examination. The measurement does not provide a material property as its value is dependent on local conditions and the actual stresses have little relationship to the average stress value. This demonstrates that there is a need for the standardization of test procedures for the measurement of bond strengths so that a universally valid comparison between different bonding agents can be performed.