Mechanics analysis of molar tooth splitting

XFEM for Composites, Biological, and Bioinspired Materials: A Review

The eXtended finite element method (XFEM) is a powerful tool for structural mechanics, assisting engineers and designers in understanding how a material architecture responds to stresses and consequently assisting the creation of mechanically improved structures. The XFEM method has unraveled the extraordinary relationships between material topology and fracture behavior in biological and engineered materials, enhancing peculiar fracture toughening mechanisms, such as crack deflection and arrest. Despite its extensive use, a detailed revision of case studies involving XFEM with a focus on the applications rather than the method of numerical modeling is in great need. In this review, XFEM is introduced and briefly compared to other computational fracture models such as the contour integral method, virtual crack closing technique, cohesive zone model, and phase-field model, highlighting the pros and cons of the methods (e.g., numerical convergence, commercial software implementation, pre-set of crack parameters, and calculation speed). The use of XFEM in material design is demonstrated and discussed, focusing on presenting the current research on composites and biological and bioinspired materials, but also briefly introducing its application to other fields. This review concludes with a discussion of the XFEM drawbacks and provides an overview of the future perspectives of this method in applied material science research, such as the merging of XFEM and artificial intelligence techniques.

On edge chipping in molar teeth from blunt occlusal contact

Edge chipping is a leading failure mode in dental teeth. Virtually all chipping studies are limited to Vickers indentation on polished cusps of molar teeth. Such works are here extended to spherical contact. Occlusal loads are applied on the tooth's central fossa or a polished cusp using ball radii ranging from 0.4 to 5.16 mm. The chip dimensions are characterized by h/Dm and D/Dm, where h, D and Dm denote indent distance, chip size and tooth crown diameter. For the fossa loading, h/Dm, D/Dm and the least chipping force Pch are virtually independent of ball radius r for r < ≈ 4 mm. In this range, h/Dm and D/Dm lie between ≈0.30 to 0.36 and 0.51 to 0.69, respectively, while Pch equals ≈1330 N. For r > ≈ 4 mm, the failure occurs by debonding of enamel sectors from the dentin core. In the case of cusp loading, h/Dm < ≈ 0.3 while D/Dm and Pch vary with r. For relatively small h or large r, the failure occurs as soon as radial cracks initiate under the loading point. For a load applied near a cusp tip, the failure occurs by enamel debonding. Finally, the present work is easily extendable to fossil teeth of hominins and apes as well as prosthetic teeth. The morphological features obtained in such studies should provide quantitative means to assess the relationships between chip dimensions, chipping force and diet characteristics.

Biomechanical perspectives on dentine cracks and fractures: Implications in their clinical management

OBJECTIVES

The present review discussed the biomechanical properties of cracks and fractures in crown and root dentine and attempted to explain why cracked teeth and vertical root fractures are so frequent despite the existence of multiple crack toughening mechanisms in dentine. The implications of this knowledge were used to justify how these defects are managed clinically.

DATA, SOURCES AND STUDY SELECTION

Literature search was conducted on PubMed, Web of Science, and Scopus for a narrative review on fracture mechanics of crown and root dentine as well as the clinical management of cracked teeth and teeth with vertical root fracture.

CONCLUSIONS

Although dentine is tougher and less brittle than enamel, it's facture toughness is considerably lower than most ductile metals. Because the initiation toughness of dentine is very low, cracks initiate from incipient damage under low stress While crack toughening mechanisms exist that enable dentine to resist crack extension, these mechanisms are often inadequate for protecting dentine from crack propagation that ultimately leads to catastrophic failure. Additional factors such as ageing also reduces the resistance of dentine to crack growth. Because dentine cracks are eventually filled with bacteria biofilms upon exposure to oral fluids, they enable rapid bacteria ingress into the dental pulp via open dentinal tubules. To date, treatment options for cracked teeth are limited. While most teeth with vertical root fracture are recommended for extraction, new strategies have been reported that appeared to achieve short-term success in preserving these teeth.

CLINICAL SIGNIFICANCE

Current strategies for the management for dentine cracks and fractures are limited and their long-term effectiveness remain uncertain. Understanding the characteristics, toughening mechanism and weakening factors of tooth cracks is helpful in designing better treatment.

An improved Smoothed Particle Hydrodynamics (SPH) method for modelling the cracking processes of teeth and its applications

The present work aims to propose a meshless method to establish the tooth meso-structures and model the tooth fracturing processes as well as investigate the influencing factors that affect the dental mechanical properties. To this end, the traditional kernel function in the SPH method has been improved by introducing a fracture mark ξ to realize the progressive failure processes of teeth; The "Particle Searching Method" has been proposed, which can realize the establishments of microstructures of teeth such as enamel, dentine, pulp, PDL and alvedar bones. The Weibull function is introduced to represent the heterogeneity of teeth, which can realize the random distribution characteristics of dental mechanical parameters. The simulation results of homogeneous and heterogeneous teeth show that the failure mode changes from tensile splitting (homogeneous) to shear failure (heterogeneous). Meanwhile, the fracture networks become more complex, and the failure stress decreases sharply. The cuspal angles also have a great impact on the teeth fracture characteristics. The failure modes changes from tensile splitting of the enamel tip to the cracking from the contact points between the enamel and the rigid ball; Different fssural morphologies have little influences on the teeth failure characteristics. The research results can provide some references for the applications of SPH method into biomechanical simulations such as teeth failure. Meanwhile, it can also provide some guidance for the understandings of the internal mechanisms of teeth fracture processes, the diagnosis and treatments of clinical diseased teeth as well as the design of bionic teeth materials.

Effect of supporting dies' mechanical properties on fracture behavior of monolithic zirconia molar crowns

The aim of this study was to investigate the effects of supporting dies with different mechanical properties on the fracture strengths and failure modes of monolithic zirconia crowns, and identify a suitable die material for testing high-strength ceramic restorations. Thirty six dies from teeth, porous titanium and composite-resin with 36 zirconia crowns were fabricated based on 3D model. Crowns were cemented, then underwent load-to-fracture testing. Fractographic analysis was performed with scanning electron microscopy, and finite element analysis was made. During loading, a high stress concentration zone formed near the loading point and on surface of die. Cracks generated on failure penetrated the crown and extended to die in 9 teeth group specimens, while composite-resin samples exhibited fracture of both crowns and dies. All dies remained intact in porous titanium group. Fracture mode was undistinguishable in all groups. It was concluded that porous titanium appears suitable as die material for dental restorations with high fracture strength.

Fundamental mechanics of tooth fracture and wear: implications for humans and other primates

Until recently, there had been little attempt in the literature to identify and quantify the underlying mechanics of tooth durability in terms of materials engineering concepts. In humans and most mammals, teeth must endure a lifetime of sustained occlusal mastication-they have to resist fracture and wear. It is well documented that teeth are resilient, but what are the unique features that make this possible? The present article surveys recent materials engineering research aimed at addressing this fundamental question. Elements that determine the mechanics and micromechanics of tooth fracture and wear are analysed: at the macrostructural level, the geometry of the enamel shell and cuspal configuration; and at the microstructural level, interfacial weakness and property gradients. Inferences concerning dietary history in relation to evolutionary pressures are discussed.

Development of a biomechanical model for dynamic occlusal stress analysis

The use of traditional finite element method (FEM) in occlusal stress analysis is limited due to the complexity of musculature simulation. The present purpose was to develop a displacement boundary condition (DBC)-FEM, which evaded the muscle factor, to predict the dynamic occlusal stress. The geometry of the DBC-FEM was developed based on the scanned plastic casts obtained from a volunteer. The electrognathographic and video recorded jaw positional messages were adopted to analyze the dynamic occlusal stress. The volunteer exhibited asymmetrical lateral movements, so that the occlusal stress was further analyzed by using the parameters obtained from the right-side eccentric movement, which was 6.9 mm long, in the stress task of the left-side eccentric movement, which was 4.1 mm long. Further, virtual occlusion modification was performed by using the carving tool software aiming to improve the occlusal morphology at the loading sites. T-Scan Occlusal System was used as a control of the in vivo detection for the location and strength of the occlusal contacts. Data obtained from the calculation using the present developed DBC-FEM indicated that the stress distribution on the dental surface changed dynamically with the occlusal contacts. Consistent with the T-Scan recordings, the right-side molars always showed contacts and higher levels of stress. Replacing the left-side eccentric movement trace by the right-side one enhanced the simulated stress on the right-side molars while modification of the right-side molars reduced the simulated stress. The present DBC-FEM offers a creative approach for pragmatic occlusion stress prediction.

Establishment of optimal variable elastic modulus distribution in the design of full-crown restorations by finite element analysis

To establish optimal elastic modulus distribution throughout the entire all-ceramic crown, aiming at improvement of the mechanical properties of the restoration as well as the adhesive interface, seven 3D models of mandibular first premolars of zirconia monolithic and bilayer crowns and lithium disilicate monolithic and bilayer crowns were constructed. The elastic modulus distribution of 8-layer crown A referred to human enamel, B was calculated by a genetic algorithm (GA) to minimize the principle stresses on the crown, and C minimized the shear stresses at the cementing lines. After applying a static load of 600 N, the maximum principle stresses were calculated and analyzed by finite element analysis (FEA). Group C were found to have the lowest peak shear stress at the cementing line and moderate peak tensile stress in the crown. Introduction of the modified elastic modulus distribution from human enamel into the entire all-ceramic crown reinforces the mechanical properties of the whole restoration as well as the adhesive interface against chipping and debonding.

On the vital role of enamel prism interfaces and graded properties in human tooth survival

Teeth of omnivores face a formidable evolutionary challenge: how to protect against fracture and abrasive wear caused by the wide variety of foods they process. It is hypothesized that this challenge is met in part by adaptations in enamel microstructure. The low-crowned teeth of humans and some other omnivorous mammals exhibit multiple fissures running longitudinally along the outer enamel walls, yet remain intact. It is proposed that inter-prism weakness and enamel property gradation act together to avert entry of these fissures into vulnerable inner tooth regions and, at the same time, confer wear resistance at the occlusal surface. A simple indentation experiment is employed to quantify crack paths and energetics in human enamel, and an extended-finite-element model to evaluate longitudinal crack growth histories. Consideration is given as to how tooth microstructure may have played a vital role in human evolution, and by extension to other omnivorous mammals.

Breaking crown dentine in whole teeth: 3D observations of prevalent fracture patterns following overload

Teeth with intact crowns rarely split or fracture, despite decades of cyclic loading and occasional unexpected overload. This is largely attributed to the presence of dentine, since cracking and fracture of enamel have been frequently reported. Dentine is similar to bone, comprising mineralised collagen fibres as a main constituent. Unlike cortical bone, however, where microcracking and damage arrest are essential for re/modelling and healing, dentine can neither remodel nor regenerate. This raises questions regarding the evolutionary benefits of toughening, leading to uncertainty whether cracks actually appear in dentine in situ. Here we study the notion that circumpulpal dentine is usually protected against, rather than damaged by severe overloads, even though it is not much more massive or stronger than it needs to be. To address this, we examined hydrated teeth still within whole jawbones of freshly-slaughtered skeletally mature pigs, mechanically loaded until fracture. Force displacement curves, optical and electron microscopy combined with 3D microstructural analysis by conventional micro-computed tomography (μCT) revealed mostly brittle fracture paths in circumpulpal crown dentine. Once overload cracks reach this mass of dentine they propagate rapidly along straight paths often parallel to the enamel flanks of the oblong shovel shaped premolars. We find infrequent signs of active toughening mechanisms with minimal crack diversion, ligament bridging and microcracking. When such toughening is seen, it mainly appears in softer dentine in the root, or near the dentine-enamel-junction (DEJ) in mantle dentine. We observed shear bands in overloaded circumpulpal dentine, due to mutual gliding of upper and lower segments. These shear bands are formed as periodic arrays of rotated dentine fragments. The 3D data consistently demonstrate the importance of the layered tooth structure, containing a stiff outer enamel shell, a soft sub-DEJ interlayer and a stiff circumpulpal dentine bulk, for deflecting cracks from splitting the tooth.

Fracture behavior of Bi-structure fiber-reinforced composite restorations

OBJECTIVE

The aim of this study was to evaluate the fracture-behavior of direct composite restorations made with two different composite-core materials. In addition, fracture toughness (FT), flexural strength (FS) and flexural modulus (FM) of tested composites were evaluated.

METHODS

Twenty groups of posterior crown restorations were fabricated (n = 6/group). The groups were made of a 4-5 mm layer of composite-core materials (everX Flow and SDR Flow⁺) and covered by a 2 mm layer of conventional composite (G-aenial Anterior & Posterior, G-aenial Universal Injectable, Essentia, CeramX, Filtek Z500). Control groups were only made of conventional composites or composite-core materials. Crowns were statically loaded until fracture. Failure-modes were then visually examined. FT, FS and FM were determined for each tested composite (n = 6).

RESULTS

ANOVA revealed that crown restorations made only from everX Flow composite had significantly higher load-bearing capacities (3866 ± 263 N) (p < 0.05) among all the groups tested. No statistically significant differences were found in the load-bearing capacities between crowns made with different composite-core materials (p > 0.05). everX Flow exhibited the highest FT (2.8 MPa m^1/2) and Z500 presented the highest FS values (197 MPa) (p < 0.05) among tested composites. With regard to the failure-mode analysis, crowns that had a fiber-reinforced core material of everX Flow revealed delaminating of surface conventional composite from the substructure layer. While in crowns that had a core material of SDR Flow⁺ or having only conventional composites with no fiber reinforcement, showed a crushing fracture pattern.

CONCLUSION

Restorations combining a fiber-reinforced composite core and a surface layer of conventional composite, displayed promising performance related to fracture-behavior.

Wear of ceramic-based dental materials

An investigation is made of wear mechanisms in a suite of dental materials with a ceramic component and tooth enamel using a laboratory test that simulates clinically observable wear facets. A ball-on-3-specimen wear tester in a tetrahedral configuration with a rotating hard antagonist zirconia sphere is used to produce circular wear scars on polished surfaces of dental materials in artificial saliva. Images of the wear scars enable interpretation of wear mechanisms, and measurements of scar dimensions quantify wear rates. Rates are lowest for zirconia ceramics, highest for lithium disilicate, with feldspathic ceramic and ceramic-polymer composite intermediate. Examination of wear scars reveals surface debris, indicative of a mechanism of material removal at the microstructural level. Microplasticity and microcracking models account for mild and severe wear regions. Wear models are used to evaluate potential longevity for each dental material. It is demonstrated that controlled laboratory testing can identify and quantify wear susceptibility under conditions that reflect the essence of basic occlusal contact. In addition to causing severe material loss, wear damage can lead to premature tooth or prosthetic failure.

Modelling of stress distribution and fracture in dental occlusal fissures

The aim of this study was to investigate the fracture behaviour of fissural dental enamel under simulated occlusal load in relation to various interacting factors including fissure morphology, cuspal angle and the underlying material properties of enamel. Extended finite element method (XFEM) was adopted here to analyse the fracture load and crack length in tooth models with different cusp angles (ranging from 50° to 70° in 2.5° intervals), fissural morphologies (namely U shape, V shape, IK shape, I shape and Inverted-Y shape) and enamel material properties (constant versus graded). The analysis results showed that fissures with larger curved morphology, such as U shape and IK shape, exhibit higher resistance to fracture under simulated occlusal load irrespective of cusp angle and enamel properties. Increased cusp angle (i.e. lower cusp steepness), also significantly enhanced the fracture resistance of fissural enamel, particularly for the IK and Inverted-Y shape fissures. Overall, the outcomes of this study explain how the interplay of compositional and structural features of enamel in the fissural area contribute to the resistance of the human tooth against masticatory forces. These findings may provide significant indicators for clinicians and technicians in designing/fabricating extra-coronal dental restorations and correcting the cuspal inclinations and contacts during clinical occlusal adjustment.

The effect of resistance grooves on the fracture toughness of zirconia-based crowns from mono and cyclic loading

Objective:

Prosthetic molar crowns in service are subjected to chewing loads, which cause a shift or dislodgment. The objective of this study is to investigate whether the addition of resistance grooves to the proximal surfaces of the abutment teeth would enhance the fracture resistance of the zirconia crowns and to compare between the patterns of cracks development on the zirconia crowns after the application of mono loading versus cyclic loading forces.

Materials and Methods:

Thirty-six all-ceramic zirconia cored crowns were prepared on the same abutment. Resistance grooves were added to the mesial and distal surfaces of 16 abutments. Before testing, all specimens subjected to thermal aging. Two groups of crowns were then subjected to cyclic axial and lateral forces for 1,250,000 cycles in aqueous conditions. Two groups of samples were also tested in monoloading fashion.

Results:

The crack pattern between mono and cyclic loading were compared. The crown fracture resistance was compared in the two types of abutments, with and without grooves. The results confirmed that the grooves addition had no effect on critical conditions to initiate failure in the case of mono loading. In cyclic loading, grooves addition increased the critical loads in the order of two. Failure patterns and location were obtained.

Conclusions:

The results showed that the location of retention grooves halted the failure in the surfaces where it was located in all loading mechanisms used in this study.

Evaluating dental zirconia

OBJECTIVES

To survey simple contact testing protocols for evaluating the mechanical integrity of zirconia dental ceramics. Specifically, to map vital material property variations and to quantify competing damage modes.

METHODS

Exploratory contact tests are conducted on layer structures representative of zirconia crowns on dentin.

RESULTS

Sharp-tip micro- and nano-indentations were used to investigate the roles of weak interfaces and residual stresses in veneered zirconia, and to map property variations in graded structures. Tests with blunt sphere indenters on flat specimens were used to identify and quantify various critical damage modes in simulated occlusal loading in veneered and monolithic zirconia.

SIGNIFICANCE

Contact testing is a powerful tool for elucidating the fracture and deformation modes that control the lifetimes of zirconia dental ceramics. The advocated tests are simple, and provide a sound physical basis for analyzing damage resistance of anatomically-correct crowns and other complex dental prostheses.

Impact of cusp inclinations on dental fractures in cracked tooth syndrome model and relevant risk evaluation

We explored the impact of cusp inclinations on dental fractures in cracked tooth syndrome model and formulated corresponding risk scale. Forty maxillary premolars were randomized into four groups for cusp inclination measurements by digital radiovisiography (RVG). For cracked tooth models, buccal and palatal cusp inclinations were achieved by grinding in groups I (59°-50°), II (64°-55°) and III (69°-60°), with group IV as blank control. All groups underwent compression loading test, with fracture levels recorded for statistical analysis. The fracture modes included a majority of crown root fractures and a minority of crown fractures in groups I and II, exclusive crown root fractures in group III, and exclusive crown fractures in group IV. Overall, palatal fractures were predominant versus buccal fractures, with exclusive palatal fractures in group IV, and oblique fractures were overwhelming versus the scanty vertical fractures. Fracture risk classification: grade III was prevalent in groups I and II, grade IV in group III, and grades I and II in group IV only. The fracture risk scores in groups III and IV had significant statistical differences versus groups I and II (P<0.05), with insignificant differences between groups I and II, respectively (P>0.05). Cracked teeth are more vulnerable to complex fractures, with increment of cusp inclinations contributable to complex fracture modes, involving deep roots and high risk scores.

On the evolutionary advantage of multi-cusped teeth

A hallmark of mammalian evolution is a progressive complexity in postcanine tooth morphology. However, the driving force for this complexity remains unclear: whether to expand the versatility in diet source, or to bolster tooth structural integrity. In this study, we take a quantitative approach to this question by examining the roles of number, position and height of multiple cusps in determining sustainable bite forces. Our approach is to use an extended finite-element methodology with due provision for step-by-step growth of an embedded crack to determine how fracture progresses with increasing occlusal load. We argue that multi-cusp postcanine teeth are well configured to withstand high bite forces provided that multiple cusps are contacted simultaneously to share the load. However, contact on a single near-wall cusp diminishes the strength. Location of the load points and cusp height, rather than cusp number or radius, are principal governing factors. Given these findings, we conclude that while complex tooth structures can enhance durability, increases in cusp number are more likely to be driven by the demands of food manipulation. Structural integrity of complex teeth is maintained when individual cusps remain sufficiently distant from the side walls and do not become excessively tall relative to tooth width.

On the importance of aging to the crack growth resistance of human enamel

With improvements in oral health and an overall increase in quality of life, the percentage of fully or largely dentate seniors is increasing. Understanding the effects of aging on the mechanical properties of teeth is essential to the maintenance of lifelong oral health. In this investigation the effects of aging on the fracture toughness of human enamel were evaluated from incremental crack growth experiments performed on tissue of donor teeth representing "young" (17 ⩽ age ⩽ 25) and "old" (age ⩾ 55) age groups. Results showed that the old enamel exhibited significantly lower resistance to fracture than that of the young tissue in two orthogonal directions of crack growth. For crack growth transverse to the enamel rods, the fracture toughness of the old enamel (0.37 ± 0.15 MPa m(0.5)) was nearly 70% lower than that of tissue from the young teeth (1.23 ± 0.20 MPa m(0.5)). Based on results from a mechanistic analysis of crack growth, the reduction in fracture resistance is attributed to a decrease in the degree of extrinsic toughening. The practice of restorative dentistry should account for these changes in tooth tissues in the treatment of senior patients.

STATEMENT OF SIGNIFICANCE

The mechanical behavior of enamel has been studied for over 3 decades. Due to the limited volume of tissue available for evaluation, past work has been largely based on indentation methods. In this investigation we have evaluated the resistance to fracture of human enamel using a conventional fracture mechanics approach and incremental crack growth. We compared the fracture resistance of cuspal enamel obtained from the teeth of representative "young" and "old" donor groups. Our results show that there is a substantial reduction in the resistance to fracture with age, that it is anisotropic, and that the degradation is more severe than that which occurs to dentin. As such, we feel this work is a significant contribution to the field.

Fracture-resistant monolithic dental crowns

OBJECTIVE

To quantify the splitting resistance of monolithic zirconia, lithium disilicate and nanoparticle-composite dental crowns.

METHODS

Fracture experiments were conducted on anatomically-correct monolithic crown structures cemented to standard dental composite dies, by axial loading of a hard sphere placed between the cusps. The structures were observed in situ during fracture testing, and critical loads to split the structures were measured. Extended finite element modeling (XFEM), with provision for step-by-step extension of embedded cracks, was employed to simulate full failure evolution.

RESULTS

Experimental measurements and XFEM predictions were self-consistent within data scatter. In conjunction with a fracture mechanics equation for critical splitting load, the data were used to predict load-sustaining capacity for crowns on actual dentin substrates and for loading with a sphere of different size. Stages of crack propagation within the crown and support substrate were quantified. Zirconia crowns showed the highest fracture loads, lithium disilicate intermediate, and dental nanocomposite lowest. Dental nanocomposite crowns have comparable fracture resistance to natural enamel.

SIGNIFICANCE

The results confirm that monolithic crowns are able to sustain high bite forces. The analysis indicates what material and geometrical properties are important in optimizing crown performance and longevity.