复合树脂固化收缩应力对黏结强度影响的三维有限元分析

目的：分析复合树脂固化收缩后黏结层的应力变化。方法：建立三维环形有限元模块，分别采用釉质、黏结剂、树脂的材料参数，应用温度应力的原理，模拟树脂固化时产生的体积收缩。分析10GPa、20GPa弹性模量的复合树脂在1％、1，5％、2％、2．5％、3％、3．5％体积收缩率时黏结层的应力分布和变化规律。结果：树脂固化时体积收缩率越大，在黏结层产生的应力越大；树脂的弹性模量越大，黏结层的应力越大。结论：树脂固化时的体积收缩可在黏结层产生较大的应力，影响黏结强度。     

Polymerization shrinkage and elasticity of flowable composites and filled adhesives.

OBJECTIVES: The magnitude and kinetics of polymerization shrinkage, together with elastic modulus, may be potential predictors of bond failure of adhesive restorations. This study examined these properties in visible-light-cured resins, in particular new flowable composites and filled adhesives. METHODS: Polymerization shrinkage values were obtained by digital video imaging before and after light-curing; shrinkage kinetics were obtained by the "deflecting disk" method and the elastic modulus by analysis of the fundamental period of vibration. RESULTS: Flowable composites generally showed higher shrinkage than traditional non-flowable composites, while more densely filled adhesives presented lower shrinkage than lightly filled or unfilled resins. The elastic moduli of flowable composites were in the low-medium range, whilst the hybrid composites showed the highest values and the microfilled the lowest. More densely filled adhesives were more rigid than lightly filled and unfilled adhesives. The kinetics behavior was material dependent, mainly characterized by the coefficient of near-linear contraction between 10 and 40% of the final shrinkage and the time to reach 75% of the final shrinkage. SIGNIFICANCE: The higher shrinkage of flowable composites over that of hybrids may indicate a potential for higher interfacial stresses. However, their lower rigidity may be a counteracting factor. The microfilled composite showed low shrinkage and low rigidity, a combination that may prove less damaging to the interface. As the kinetics parameters tended to be material specific, no specific class of materials should be seen as more stress inducing until studies determine the relative importance of each examined parameter. The performance of adhesive resins as stress buffers also remains unpredictable.     

Shear versus micro-shear bond strength test: a finite element stress analysis.

OBJECTIVES: This study aimed at comparing the stress distribution in shear and micro-shear test set-ups using finite element analysis, and suggesting some parameter standardization that might have important influence on the results. METHODS: Two-dimensional plane strain finite element analysis was performed using MSCPatran and MSCMarc softwares. Model configurations were based on published experimental shear and micro-shear test set-ups and material properties were assumed to be isotropic, homogeneous and linear-elastic. Typical values of elastic modulus and Poisson's ratios were assigned to composite, dentin and adhesive. Loading conditions considered a single-node concentrated load at different distances from the dentin-adhesive interface, and proportional geometry (1:5 scale, but fixed adhesive layer thickness in 50microm) with similar calculated nominal strength. The maximum tensile and shear stresses, and stress distribution along dentin-adhesive interfacial nodes were analyzed. RESULTS: Stress distribution was always non-uniform and greatly differed between shear and micro-shear models. A pronounced stress concentration was observed at the interfacial edges due to the geometric change: stress values farther exceeded the nominal strength and tensile stresses were much higher than shear stresses. For micro-shear test, the relatively thicker adhesive layer and use of low modulus composites may lead to relevant stress intensification. An appropriate loading distance was established for each test (1mm for shear and 0.1mm for micro-shear) in which stress concentration would be minimal, and should be standardized for experimental assays. SIGNIFICANCE: The elastic modulus of bonded composites, relative adhesive layer thickness and load application distance are important parameters to be standardized, once they influence stress concentration.     

Stress distributions in adhesively cemented ceramic and resin-composite Class II inlay restorations: a 3D-FEA study.

OBJECTIVES: The purpose of this study was to investigate the effect of differences in the resin-cement elastic modulus on stress-transmission to ceramic or resin-based composite inlay-restored Class II MOD cavities during vertical occlusal loading. METHODS: Three finite-element (FE) models of Class II MOD cavity restorations in an upper premolar were produced. Model A represented a glass-ceramic inlay in combination with an adhesive and a high Young's modulus resin-cement. Model B represented the same glass-ceramic inlay in combination with the same adhesive and a low Young's modulus resin-cement. Model C represented a heat-cured resin-composite inlay in combination with the same adhesive and the same low Young's modulus resin cement. Occlusal vertical loading of 400 N was simulated on the FE models of the restored teeth. Ansys FE software was used to compute the local von Mises stresses for each of the models and to compare the observed maximum intensities and distributions. Experimental validation of the FE models was conducted. RESULTS: Complex biomechanical behavior of the restored teeth became apparent, arising from the effects of the axial and lateral components of the constant occlusal vertical loading. In the ceramic-inlay models, the greatest von Mises stress was observed on the lateral walls, vestibular and lingual, of the cavity. Indirect resin-composite inlays performed better in terms of stress dissipation. Glass-ceramic inlays transferred stresses to the dental walls and, depending on its rigidity, to the resin-cement and the adhesive layers. For high cement layer modulus values, the ceramic restorations were not able to redistribute the stresses properly into the cavity. However, stress-redistribution did occur with the resin-composite inlays. SIGNIFICANCE: Application of low modulus luting and restorative materials do partially absorb deformations under loading and limit the stress intensity, transmitted to the remaining tooth structures.     

复合树脂固化收缩应力对釉质受力影响的三维有限元研究

解放军总医院老年口腔病科副主任医师目的:分析复合树脂固化收缩后釉质的应力变化。方法:建立三维环形有限元模块,分别采用釉质、粘结剂、树脂的材料参数,应用温度应力的原理,模拟树脂固化时的体积收缩。分别分析弹性模量10MPa树脂在1%、1.5%、2%、2.5%、3%、3.5%体积收缩率时釉质应力分布及变化规律。结果:树脂固化时体积收缩率越大,釉质受力越大;应力集中的部位在釉质粘结界面边缘;距粘结界面距离越大,应力越小;釉质部分的vonMises应力明显大于第一主应力。结论:树脂固化时,可以在釉质产生较大的应力,特别是vonMises应力。     

Prediction of composite elastic modulus and polymerization shrinkage by computational micromechanics.

OBJECTIVES: The objective of this study was to simulate the elastic modulus and polymerization shrinkage of a light activated polymer matrix composite using a generalized method of cells (GMC) micromechanics model. Two hypotheses were tested: (1) the micromechanics model provides estimates of elastic modulus vs filler fraction with greater accuracy than the rule of mixtures, Hashin-Shtrikman and phenomenological models; (2) Micromechanics Analysis Code/Generalized Method of Cells accurately simulates experimental benchmarks of polymerization shrinkage strain. METHODS: The study applied mathematical algorithms to a representative volume element of a model polymer composite to yield value estimates of the elastic modulus and contraction strain. Mechanical properties of the composite constituents were derived from thermomechanical and dynamic mechanical analysis of BisGMA and TEGDMA filled and unfilled resins. Data from the micromechanics model were compared to results of other analytical methods as well as experimental benchmarks. RESULTS: Predictions of elastic modulus vs filler fraction from the micromechanics model provided greater accuracy than the rule of mixtures and the Hashin-Shtrikman models. Predictions of polymerization shrinkage strain were within 13% of experimental values. SIGNIFICANCE: The elastic micromechanics model presented accurately predicted elastic modulus and polymerization shrinkage strain as a function of filler fraction, superior to other analytical methods.     

三维有限元法分析复合树脂收缩应力的研究

目的：研究模拟树脂的收缩应力的方法。方法：建立简单的有限元模块代表釉质、粘结剂、树脂,应用温度应力的原理,使树脂的体积产生收缩,同时利用材料力学的原理进行了可行性验证。结果：建立了模拟树脂收缩应力的模型。应力集中在弹性模量大的模块及洞形的线角部位。结论：采用温度应力的方法,可以较好的模拟收缩应力。     

Shrinkage stress and cuspal deflection in MOD restorations: analytical solutions and design guidelines

ObjectiveThis paper aimed to derive analytical solutions for the shrinkage stress and cuspal deflection in model Class-II mesial-occlusal-distal (MOD) resin-composite restorations to better understand their dependence on geometrical and material parameters. Based on the stress solutions, it was shown how design curves could be obtained to guide the selection of dimensions and materials for the preparation and restoration of this class of cavities.MethodsThe cavity wall was considered as a cantilevered beam while the resin composite was modeled as Winkler’s elastic foundation with closely-spaced linear springs. Further, a mathematical model that took into account the combined effect of material properties, sample geometry and compliance of the surrounding constraint was employed to relate the shrinkage stress at the “tooth-composite” interface to the local compliance of the cavity wall. Exact analytical solutions were obtained for cuspal deflection and shrinkage stress along the cavity wall by solving the resulting differential equation, which had the same form as that for a beam on elastic foundation with a distributed load. To quantify the shrinkage stress at the cavity floor, the resin composite was assumed to be a beam, fixed at both ends and loaded with a uniformly distributed load that approximated the shrinkage stress. The analytical solutions thus obtained were compared with results from finite element analysis (FEA).ResultsThe analytical solution for cuspal deflection contains a dimensionless parameter, γ, which represents the stiffness of the cavity wall relative to that of the cured resin composite. For the same shrinkage strain, cuspal deflection increases with reducing γ, i.e. reducing stiffness of the cavity wall or increasing stiffness of the composite. For the same γ, cuspal deflection increases proportionally with shrinkage strain. Shrinkage stress along the cavity wall is maximum at the cavity corner and reduces towards the occlusal surface; the maximum value depends only on Young’s modulus and the shrinkage strain of the resin composite. For low values of γ, the interfacial stress at the occlusal surface can become compressive. The interfacial stress at the cavity floor can be much higher than that along the cavity wall, increasing exponentially with the resin composite’s thickness. The analytical solutions agree well with FEA predictions.SignificanceWhen validated, the analytical solutions and design curves presented in this study can provide useful guidelines for choosing appropriate dimensions of cavity preparations and resin composite materials with suitable mechanical properties for Class-II MOD restorations to help avoid tooth fracture and interfacial debonding caused by polymerization shrinkage.     

Residual shrinkage stress distributions in molars after composite restoration.

OBJECTIVE: Experimental measurements on various restoration configurations have shown that restored teeth deform under the influence of polymerization shrinkage, but actual residual stresses could not be determined. The purpose of this study was to calculate and validate shrinkage stresses associated with the reported tooth deformations. METHODS: Three different restoration configurations were applied in a finite element model of a molar. The composite properties were based on experimentally determined composite behavior during polymerization. The occlusal deformation pattern and the residual stress states of the tooth, restoration, and tooth-restoration interface were calculated using a polymerization model based on the post-gel shrinkage concept. Reported strain gauge measurements and occlusal deformation patterns were used for validation. RESULTS: The shrinkage stresses depended on the configuration and size of the restorations. The tooth's resistance against polymerization shrinkage diminished with loss of dental hard tissue. Larger restorations resulted in lower stress levels in the restoration and tooth-restoration interface, but increased stresses in the tooth. The maximum stress values found for different configurations were not decisively different. SIGNIFICANCE: The validated model indicated that shrinkage stress cannot be based on composite properties or restoration configuration alone, but has to be approached as a distributed pattern that depends on the location and on the properties of tooth and restoration, geometry, constraints, and restoration procedures. Tooth deformation was indicative of stresses in the tooth rather than in the restoration or across the tooth-restoration interface.     

Contraction stress determinants in dimethacrylate composites

The influence of composite organic content on polymerization stress development remains unclear. It was hypothesized that stress was directly related to differences in degree of conversion, volumetric shrinkage, elastic modulus, and maximum rate of polymerization encountered in composites containing different BisGMA (bisphenylglycidyl dimethacrylate) concentrations and TEGDMA (triethylene glycol dimethacrylate) and/or BisEMA (ethoxylated bisphenol-A dimethacrylate) as co-monomers. Stress was determined in a tensilometer. Volumetric shrinkage was measured with a mercury dilatometer. Elastic modulus was obtained by flexural test. We used fragments of flexural specimens to determine degree of conversion by FT-Raman spectroscopy. Reaction rate was determined by differential scanning calorimetry. Composites with lower BisGMA content and those containing TEGDMA showed higher stress, conversion, shrinkage, and elastic modulus. Polymerization rate did not vary significantly, except for the lower value of the 66% TEGDMA composite. We used linear regressions to evaluate the association between polymerization stress and conversion (R(2)=0.905), shrinkage (R(2)=0.825), and modulus (R(2)=0.623).     

Cuspal flexure of teeth with composite restorations subjected to occlusal loading

PURPOSE: To measure in vitro the cuspal deflection produced by polymerization shrinkage and occlusal loading in mesio-occlusal (MO) and mesio-occlusal-distal (MOD) bonded composite restorations. MATERIALS AND METHODS: Twenty first premolars were studied, attaching a small crystal ball to each cusp vertex as a reference point for intercuspal distance measurements. MO cavities were made in ten premolars and MOD cavities in the other ten. Cavities were then restored with Syntac Single adhesive and Tetric Ceram composite in two increments. A precision micrometer was used to measure intercuspal distances in unaltered teeth (baseline distance), unaltered teeth under 150 N load, restored teeth at 5 min after restoration completion, and restored teeth under 150 N load. RESULTS: In the two study groups, both polymerization shrinkage and application of 150 N load produced a statistically significant change in intercuspal distance compared with baseline measurement. The cuspal deflection produced by 150 N load was statistically similar between unaltered and restored teeth, although polymerization shrinkage acted as a preload in the latter case (starting point was not baseline condition). The cuspal deflection produced by polymerization shrinkage and occlusal load was significantly greater in MOD than in MO restorations. CONCLUSION: The cuspal deflection produced by composite polymerization shrinkage and occlusal loading is significantly greater in MOD vs MO composite restorations.     

Handling of mechanical stresses in composite restorations.

The origin of stress in adhesive resin composite restorations is attributed to restrained shrinkage during polymerization and is dependent on the configuration of the restoration. Moreover, non-homogeneous deformations during functional loading can damage the interface as well as the coherence of the material. Damage from these stresses can be reduced by application of an elastic lining at the adhesive interfaces and by slowing the initial conversion by two-step light initiation of the resin. The various factors that mediate flow and compliance are discussed.     

Influence of elasticity on gap formation in a lining technique with flowable composite

The purpose of this study was to investigate the effect of flowable composites as liners for direct composite restorations, with key focus on the elastic moduli of flowable and condensable composites. After treating the composite mold cavity surface with an adhesive system, one of the flowable composites was placed as a 1 mm-thick layer on the cavity floor and irradiated for 20 seconds. The rest of cavity was subsequently filled with a condensable composite and irradiated for 40 seconds. Gap formation at both interfaces--between the cavity floor and flowable composite, and between the flowable and condensable composites--was examined. No gaps were detected at the interface between the cavity floor and flowable composite. Gap percentage at the interface between the flowable and condensable composites was dependent on the difference in elastic modulus. It was concluded that flowable composite with high elastic modulus could inhibit gap formation between flowable and condensable composites.     

A model for shrinkage strain in photo polymerization of dental composites.

OBJECTIVES: We formulate a new model for the shrinkage strain developed during photo polymerization in dental composites. The model is based on the diffusion type fractional order equation, since it has been proved that polymerization reaction is diffusion controlled (Atai M, Watts DC. A new kinetic model for the photo polymerization shrinkage-strain of dental composites and resin-monomers. Dent Mater 2006;22:785-91). Our model strongly confirms the observation by Atai and Watts (see reference details above) and their experimental results. The shrinkage strain is modeled by a nonlinear differential equation in (see reference details above) and that equation must be solved numerically. In our approach, we use the linear fractional order differential equation to describe the strain rate due to photo polymerization. This equation is solved exactly. RESULTS: As shrinkage is a consequence of the polymerization reaction and polymerization reaction is diffusion controlled, we postulate that shrinkage strain rate is described by a diffusion type equation. We find explicit form of solution to this equation and determine the strain in the resin monomers. Also by using equations of linear viscoelasticity, we determine stresses in the polymer due to the shrinkage. The time evolution of stresses implies that the maximal stresses are developed at the very beginning of the polymerization process. SIGNIFICANCE: The stress in a dental composite that is light treated has the largest value short time after the treatment starts. The strain settles at the constant value in the time of about 100s (for the cases treated in Atai and Watts). From the model developed here, the shrinkage strain of dental composites and resin monomers is analytically determined. The maximal value of stresses is important, since this value must be smaller than the adhesive bond strength at cavo-restoration interface. The maximum stress determined here depends on the diffusivity coefficient. Since diffusivity coefficient increases as polymerization proceeds, it follows that the periods of light treatments should be shorter at the beginning of the treatment and longer at the end of the treatment, with dark interval between the initial low intensity and following high intensity curing. This is because at the end of polymerization the stress relaxation cannot take place.     

Contraction stress of flowable composite materials and their efficacy as stress-relieving layers

BACKGROUND: The authors compared the polymerization contraction stress produced by flowable resin-based composites with stress values produced by nonflowable composites. They also measured the stress reduction produced by placing a precured layer of flowable composite under a nonflowable composite. METHODS: The authors first tested four flowable and six nonflowable composite materials for contraction stress in a tensiometer. In the second part of the study, they applied a 1.4-millimeter-thick layer of flowable composite or unfilled resin and precured it in the test apparatus to assess the stress relief produced by a low-modulus material during light curing of a subsequent layer of highly filled composite. Flexural moduli of the precured materials were determined via a three-point bending test. RESULTS: The stress values ranged between 6.04 and 9.10 megapascals. The authors found no significant differences in stress between flowable and nonflowable composites. Microfilled composites produced lower contraction stress than did hybrids. The flexural modulus of the flowable composites varied between 4.1 and 8.2 GPa. Regarding the effect of a precured layer of composite on contraction stress, the authors observed significant reductions with only one of the flowable materials and with the unfilled resin. CONCLUSIONS: The flowable composites produced stress levels similar to those of nonflowable materials. Most of the flowable materials tested did not produce significant stress reductions when used under a nonflowable composite. CLINICAL IMPLICATIONS: Using a flowable resin-based composite as a restorative material is not likely to reduce the effects of polymerization stress. When used in a thin layer under a nonflowable composite, the stress reduction depended on the elastic modulus of the lining material.     

Dynamic covalent chemistry (DCC) in dental restorative materials: Implementation of a DCC-based adaptive interface (AI) at the resin–filler interface for improved performance

ObjectiveDental restorative composites have been extensively studied with a goal to improve material performance. However, stress induced microcracks from polymerization shrinkage, thermal and other stresses along with the low fracture toughness of methacrylate-based composites remain significant problems. Herein, the study focuses on applying a dynamic covalent chemistry (DCC)-based adaptive interface to conventional BisGMA/TEGDMA (70:30) dental resins by coupling moieties capable of thiol–thioester (TTE) DCC to the resin–filler interface as a means to induce interfacial stress relaxation and promote interfacial healing.MethodsSilica nanoparticles (SNP) are functionalized with TTE-functionalized silanes to covalently bond the interface to the network while simultaneously facilitating relaxation of the filler–matrix interface via DCC. The functionalized particles were incorporated into the otherwise static conventional BisGMA/TEGDMA (70:30) dental resins. The role of interfacial bond exchange to enhance dental composite performance in response to shrinkage and other stresses, flexural modulus and toughness was investigated. Shrinkage stress was monitored with a tensometer coupled with FTIR spectroscopy. Flexural modulus/strength and flexural toughness were characterized in three-point bending on a universal testing machine.ResultsA reduction of 30% in shrinkage stress was achieved when interfacial TTE bond exchange was activated while not only maintaining but also enhancing mechanical properties of the composite. These enhancements include a 60% increase in Young’s modulus, 33% increase in flexural strength and 35% increase in the toughness, relative to composites unable to undergo DCC but otherwise identical in composition. Furthermore, by combining interfacial DCC with resin-based DCC, an 80% reduction of shrinkage-induced stress is observed in a thiol–ene system “equipped” with both types of DCC mechanisms relative to the composite without DCC in either the resin or at the resin–filler interface.SignificanceThis behavior highlights the advantages of utilizing the DCC at the resin–filler interface as a stress-relieving mechanism that is compatible with current and future developments in the field of dental restorative materials, nearly independent of the type of resin improvements and types that will be used, as it can dramatically enhance their mechanical performance by reducing both polymerization and mechanically applied stresses throughout the composite lifetime.     

Polymerization shrinkage of resin-based composites for dental restorations: A digital volume correlation study

ObjectiveResin-based composites are widely used in dental restorations; however, their volumetric shrinkage during polymerization leads to several issues that reduce the restoration survival rates. For overcoming this problem, a deep study of shrinkage phenomena is necessary.MethodsIn this study, micro-tomography (μ-CT) is combined with digital volume correlation (DVC) to investigate the effect of several factors on the polymerization strain of dental composites in model cavities: the presence/absence of an adhesive, the use of transparent/blackened cavities, and irradiation times between 1 and 40 s.ResultsThe results indicate that the presence of an adhesive at the interface between the cavity and composite does not reduce the total strain but instead limits it to a preferential direction. In addition, regardless of the conditions, the main strain is generated along the axis parallel to the polymerization irradiation (the vertical axis). Finally, the total strain appears to occur in the first 5 s of irradiation, with no further evolution observed for longer irradiation times.SignificanceThis work provides new insight into resin-based composite shrinkage and demonstrates the benefit of coupling DVC and μ-CT to better understand the degradation mechanisms of these materials.     

The effects of cavity-margin-angles and bolus stiffness on the mechanical behavior of indirect resin composite class II restorations

Objective

To study the influence of the different class II mesio-occlusal-distal (MOD) cavity shape on the stress and strain distributions in adhesive indirect restorations, using numerical finite element analysis (FEA). To investigate the relationship between restored teeth failure and stiffness of food, three values of Young’s modulus were used for the food.

Effects of polymerization shrinkage on the interfacial stress at resin-metal joint in denture-base: a non-linear FE stress analysis.

OBJECTIVES: The purpose of this study was to investigate the effects of polymerization shrinkage on stress at the interface between resin and metal in removable dentures. METHODS: Three-dimensional finite element models of a denture-base were studied, which consisted of acrylic occlusal rims with different heights and metal frameworks. A relaxation modulus of 1.5 GPa for the resin and a Young's modulus of 220 GPa for the metal were used as the material properties. Each model was constrained at the edge of the framework on the palatal vault. Surface-to-surface contact elements were used to calculate the interfacial stress in a direction perpendicular to the bond surface under a linear shrinkage ranging from 0.41 to 0.65%. The principal stress within the resin was also calculated. RESULTS: The maximum interfacial and principal stresses within the denture-base increased with resin shrinkage. Under the lowest linear shrinkage, the mean area percentages in the resin-metal joint that showed interfacial tensile stresses over 10 and 20 MPa were 63.4 and 0%, respectively. While under the highest linear shrinkage, these mean area percentages were 98.8 and 38.1%, respectively. Negligible differences in the stresses were shown by occlusal heights. SIGNIFICANCE: The polymerization shrinkage level has a significant influence on the residual stress at the resin-metal interface. Enhancement of the bond strength on the interface can reduce the failure probability at a resin-metal joint.     

Does layering minimize shrinkage stresses in composite restorations?

Polymerization shrinkage of resin composites may impair restoration longevity. It is hypothesized that layering, rather than bulk, techniques result in less stress in the tooth-restoration complex. The aim of this study was to compare shrinkage stresses for different restorative techniques used for cusp-replacing restorations with direct resin composite. In a 3-D FE model, the dynamic process of shrinkage during polymerization was simulated. Time-dependent parameters (shrinkage, apparent viscosity, Young's modulus, Poisson ratio, and resulting creep), which change during the polymerization process, were implemented. Six different restorative procedures were simulated: a chemically cured bulk technique, a light-cured bulk technique, and 4 light-cured layering techniques. When polymerization shrinkage is considered, a chemically cured composite shows the least resulting stress. The differences seen among various layering build-up techniques were smaller than expected. The results indicate that the stress-bearing locations are the interface and the cervical part of the remaining cusp.