Cohesive Fracture Research Articles

Punching Shear Response Theory (PSRT) – A two degree of freedom kinematic theory for modeling the entire punching shear vs. deformation response of RC slabs and footings

Punching failures of reinforced concrete flat slabs and footings without shear reinforcement have been responsible for a number of catastrophic collapses. Despite intense scientific efforts in recent decades that have led to failure criteria-based phenomenological models, our current mechanistic understanding is still not sufficiently advanced to fathom the physical background of punching phenomena in RC structures. That is why, this paper proposes a novel two degree of freedom mechanical theory - called Punching Shear Response Theory (PSRT) - that interconnects all relevant effects of punching shear behavior, namely strutting action within a conical concrete shell at the slab-column interface, shear transfer actions elicited along the circumferential punching shear crack, including cohesive fracture process zone behavior, aggregate interlock and dowel action of reinforcement, as well as transfer of normal forces within tangential and radial cracks between slab segments in one all-encompassing algorithm. The PSRT can thoroughly mimic and efficiently reproduce the entire punching failure process of flat slabs and squat members (footings, pile caps, column bases) including prediction of pre- and post-peak punching shear vs. deformation response, quantification of different punching shear contributions and analysis of their evolution and mutual interaction within the failure process. The paper illustrates the analytical development of the PSRT, exemplifies its ability to reproduce the punching shear response of selected benchmark problems, proves its validity by database evaluations (incl. punching strength and deformation capacity) and eventually discloses the physical causalities of punching failures in RC structures.

Multiscale modelling of bitumen-aggregate interfaces from molecular debonding to pull-off strength

Cohesive and adhesive debonding and their percentages determine an asphalt mixture's bond energy which controls the material damage process. This study aims to establish the link of the probability of cohesive debonding at the nanoscale and the percentage of cohesive cracking at the microscale. Using this link, this study also investigates the influence of external conditions on the debonding behavior of bitumen-aggregate interfaces, and proposes a modified bond theory to predict the tensile strength of the interfaces. The debonding process was investigated numerically using coarse-grained molecular dynamics (CGMD) simulations at nanoscale and experimentally by a novel pull-off test (POT) at microscale. Results show that the debonding behaviors show consistency between the simulations and the experiments under different conditions. Cohesive fracture increases with bitumen film thickness and reaches a plateau (∼80% and 100% at the nanoscale and microscale, respectively); They also increase with temperatures (rise from 72% to 81% at nanoscale and from 73% to 100% at microscale, respectively) while show no relationship with loading rates. The pull-off strength decreases with bitumen film thickness and temperatures, and increases with loading rates. The modified Kendall's model can effectively predict the debonding behavior and the pull-off strength at different conditions.

Experimental and numerical study on the mechanical behaviours of two rocks with circular openings

Abstract The presence of discontinuities in rocks can significantly compromise the performance of the rocks in terms of strength and stiffness, thereby threatening the reliability and safety of engineering structures built in or on the rocks, for example, tunnels, and slopes. In this paper, a comprehensive set of experimental tests, including Brazilian disc tests and uniaxial compression tests, were performed for two distinct rocks including granite and sandstone with seven patterns of opening holes, in addition to intact rock specimens. To investigate the micro-cracks initiation and propagation, a hybrid continuum-discrete element method incorporating a cohesive fracture model was adopted to simulate the laboratory testing. The stress–strain relations, micro-cracks initiation and propagation, Young’s modulus, compressive strength, tensile strength and micro-cracks rate and orientation were discussed. The results showed that the presence of the holes could significantly influence the tensile strength and compressive strength. However, its influence on the Young’s modulus was found to be relatively insignificant.

Improving the Performance of Wood Adhesive with Waste Rubber Tire

Reclaimed rubber (RR) from waste tires was introduced as a wood adhesive by blending with epoxidized natural rubber (ENR). To improve the polarity of RR and compatibility with ENR, maleic anhydride (MA) was grafted onto RR chains. Influences of RR and RR-g-MA (maleic anhydride grafted reclaimed rubber) on the adhesion of wood adhesive along with their properties such as crosslinking, mechanical properties, thermal stability, and wettability were studied. It was found that RR and RR-g-MA affect the vulcanization of ENR by increasing crosslink density. Especially, in the case of using RR-g-MA generates a new form of an ester linkage. The higher crosslink density together with the formation of ester linkages results in superior thermal stability by the addition of RR-g-MA. In addition, the incorporation of RR exhibited an increase in the lap shear strength when compared with the pure ENR. This improvement is due to the increased crosslink density because the presence of RR resulted in the enhanced cohesive strength of rubber adhesive. Additionally, the incorporation of RR-g-MA showed higher efficiency to improve the adhesion of rubber adhesive. The addition of RR-g-MA has not only enhanced the cohesive strength of rubber adhesive, but also increased the adhesive strength from the interaction between the hydroxy group in cellulose on the wood surface and the polar functional group (i.e., oxirane rings of ENR, maleic group of RR-g-MA and ester group of ester linkage) of rubber adhesive. Therefore, the cohesive fracture was observed in ENR/RR-g-MA adhesive. HIGHLIGHTS The worn-out rubber tire as a mass waste can be utilized to develop effective adhesives The addition of maleic anhydride grafted reclaimed rubber caused to generate new ester linkage between epoxidized natural rubber chains The epoxidized natural rubber vulcanizates with maleic anhydride grafted reclaimed rubber showed superior thermal stability The addition of maleic anhydride grafted reclaimed rubber enhanced the adhesive strength of rubber adhesive from the interaction between hydroxy group in cellulose on the wood surface and the polar functional group of rubber adhesive GRAPHICAL ABSTRACT

Microstructure- and damage-nucleation-based crystal plasticity finite element modeling for the nucleation of multi-type voids during plastic deformation of Al alloys

During deformation of aluminum (Al) alloys, there are three kinds of voids being formed by distinct mechanisms, i.e., matrix-cracking voids (MCVs), particle-cracking voids (PCVs), and interface-debonding voids (IDVs), due to mesoscale heterogeneous deformation. The three kinds of void nucleation have different effects on the subsequent void growth, void coalescence, and ductile fracture of Al alloys. To determine the complex nucleation behavior of the three kinds of voids under mesoscale heterogeneous deformation, a microstructure- and damage-nucleation-based crystal plasticity finite element (MDNCPFE) model considering different nucleation mechanisms was established. To realize the MDN-CPFE modeling, the deformation and void nucleation of the matrix, particle, and their interface in Al alloys were described by a non-local dislocation density CP constitutive model and a local stored energy density criterion, an elastic constitutive model and a maximum principal stress criterion, and a cohesive zone model and fracture energy criterion, respectively. The developed MDN-CPFE model was validated by the nucleation locations and quantitative variations of the three kinds of voids in an in-situ tensile test. Using the developed model, the nucleation characteristics of the three kinds of voids during the small deformation of Al alloys were analyzed. It is found that PCVs are likely to nucleate within particles that are located at the deformation bands and with greater shape irregularity; IDVs are prone to nucleate at the interfaces around smaller particles in the deformation bands; MCVs tend to nucleate within grains with a higher Schmid factor and aspect ratio. The void area fractions (VAFs) of the three kinds of voids all evolve with an incubation stage and then followed by an exponentially increasing stage during deformation. The duration of the incubation stage for the three kinds of voids, designated by the nucleation strain, presents the following sequence: PCV < IDV < MCV; while, their VAFs and quantities present the opposite sequence. Additionally, the effects of the particle volume fraction and grain size on the nucleation strain, total VAF, and proportion of VAFs of the three kinds of voids were unraveled.

Antibacterial and physical properties of resin cements containing MgO nanoparticles

Cariogenic bacteria and dental plaque biofilm at prosthesis margins are considered a primary risk factor for failed restorations. Resin cement containing antibacterial agents can be beneficial in controlling bacteria and biofilm. This work aimed to evaluate the impact of incorporating magnesium oxide nanoparticles (MgONPs) as an antibacterial filler into dual-cure resin cement on bacteriostatic activity and physical properties, including mechanical, bonding, and physicochemical properties, as well as performance when subjected to a 5000-times thermocycling regimen. Experimental resin cements containing MgONPs of different mass fractions (0, 2.5%, 5%, 7.5% and 10%) were developed. Results suggested that the inclusion of MgONPs markedly improved the materials’ bacteriostatic effect against Streptococcus mutans without compromising the physical properties when its addition reached 7.5 wt%. The mechanical properties of the specimens did not significantly decline after undergoing aging treatment, except for the flexural properties. In addition, the cements displayed good bonding performance and the material itself was not prone to cohesive fracture in the failure mode analysis. Furthermore, MgONPs possibly have played a role in decelerating material aging during thermocycling and enhancing bonding fastness in the early stage of cementation, which requires further investigation. Overall, developing MgONPs-doped resin cements can be a promising strategy to improve the material's performance in inhibiting cariogenic bacteria at restoration margins, in order to achieve a reduction in biofilm-associated secondary caries and a prolonged restoration lifespan.

A comparative analysis of continuum plasticity, viscoplasticity and phase-field models for earthquake sequence modeling

This paper discusses continuum models for simulating earthquake sequences on faults governed by rate-and-state dependent friction. Through detailed numerical analysis of a conventional strike-slip fault, new observations regarding the use of various continuum earthquake models are presented. We update a recently proposed plasticity-based model using a consistently linearized formulation, show its agreement with discrete fault models for fault thicknesses of hundreds of meters, and demonstrate mesh objectivity for slip-related variables. To obtain a fully regularized fault width description with an internal length scale, we study the performance and mesh convergence of a plasticity-based model complemented by a Kelvin viscosity term and the phase-field approach to cohesive fracture. The Kelvin viscoplasticity-based model can introduce an internal length scale and a mesh-objective response. However, on grid sizes down to meters, this only holds for very high Kelvin viscosities that inhibit seismic slip rates, which renders this approach impractical for simulating earthquake sequences. On the other hand, our phase-field implementation for earthquake sequences provides a numerically robust framework that agrees with a discrete reference solution, is mesh objective, and reaches seismic slip rates. The model, unsurprisingly, requires highly refined grids around the fault zones to reproduce results close to a discrete model. Following this line, the effect of an internal length scale parameter on the phase-field predictions and mesh convergence are discussed.

Simulation of low-temperature brittle fracture of asphalt mixtures based on phase-field cohesive zone model

In this study, a phase-field cohesive zone model (CZM) was presented to simulate the low-temperature brittle fracture of asphalt mixture by finite element method (FEM). The phase-field CZM was applied directly to simulate low-temperature homogeneous fracture of asphalt mixtures. Furthermore, a combination method was proposed for the heterogeneous fracture analysis of asphalt mixtures at low temperature. In this method, the phase-field CZM and the conventional interface CZM are used to simulate the cohesive fracture within the fine aggregate matrix (FAM) and the adhesive fracture at the FAM-aggregate interface, respectively. Then, the applicability of the phase-field CZM to simulate mixed-mode fracture in asphalt mixtures was analyzed by the single-edge notch beam tests with different notch offsets. Furthermore, the cohesive fracture simulation of asphalt mixture based on phase-field CZM and interface CZM was compared. The results indicate that the numerical results based on the phase-field CZM in both homogeneous and heterogeneous fracture analysis are in good agreement with the experimental results. The softening curve of the interface CZM gradually converges to that of the phase-field CZM as the adhesive stiffness increases. Under the same traction-separation law, the crack path predicted by the combination method is similar to that of the pure CZM method. However, the combination method shows a more pronounced brittle behavior of the material. In addition, the combination method has higher computational efficiency and requires less computational memory. In summary, this study provides an effective method to simulate homogeneous and heterogeneous brittle fracture of asphalt mixture at low temperatures.

Three-dimensional numerical simulation of hydraulically driven cohesive fracture propagation in deformable reservoir rock using enriched EFG method

Three-dimensional numerical simulation of hydraulically driven cohesive fracture propagation in deformable reservoir rock using enriched EFG method

Effects of posttreatment on the metal-ceramic bond properties of selective-laser-melted Co-Cr dental alloy—Part 2: Heat treatment after porcelain firing

Statement of problemThe selective laser melting (SLM) technique has been a promising method of fabricating Co-Cr metal-ceramic restorations; however, the lower metal-ceramic bond properties of SLM Co-Cr restorations have become a major issue in clinical use. PurposeThe purpose of this in vitro study was to propose and verify a method of improving the metal-ceramic bond properties of SLM Co-Cr alloy with heat treatment after porcelain firing (PH). Material and methodsForty-eight (25×3×0.5 mm) Co-Cr specimens, divided into 6 groups (Control group [CG]; 550 °C; 650 °C; 750 °C; 850 °C; 950 °C) according to PH temperatures, were prepared by using SLM techniques. The 3-point bend tests were performed to evaluate the metal-ceramic bond strengths; subsequently, the fracture feature was assessed by using a digital camera and scanning electron microscope (SEM) coupled with an energy-dispersive X-ray spectroscopy (EDS) detector, to determine the area fraction of adherence porcelain (AFAP). The interface morphologies and element distribution were determined with SEM/EDS detectors. Phase identification and quantification were examined with an X-ray diffractometer (XRD). A 1-way ANOVA and the Tukey honestly significant difference tests were used to analyze bond strengths and AFAP values (α=.05). ResultsThe bond strengths were 35.33 ±1.25 MPa for the CG group, 34.53 ±3.20 MPa for the 550 °C group, 38.20 ±2.60 MPa for the 650 °C group, 42.85 ±2.31 MPa for the 750 °C group, 33.28 ±3.85 MPa for the 850 °C group, and 29.09 ±2.86 MPa for the 950 °C group. Significant differences were not observed among the CG, 550 °C, and 850 °C groups (P>.05) but were found among the other groups (P<.05). Fracture and AFAP results displayed a mixed fracture mode of adhesive and cohesive fracture. The thicknesses of native oxide films across the 6 groups were relatively close as the temperature increased, but the thickness of the diffusion layer increased as well. Excessive oxidation and massive phase transformation caused holes and microcracks to appear in the 850 °C and 950 °C groups, reducing bond strengths. XRD analysis evidenced that the phase transformation of γ→ε occurred at the interface during PH treating. ConclusionsPH treatment significantly affected the metal-ceramic bond properties of SLM Co-Cr porcelain specimens. The 750 °C-PH-treated specimens displayed higher mean bond strengths and improved fracture characteristics among the 6 groups.

Cohesive failure modeling based on the phase‐field approach

AbstractRegarding resolving the crack‐induced strong discontinuity problems, e.g., crack faces separating, contact and friction, the recent established approach based on the Representative Crack Element (RCE) framework is developed to describe a robust crack kinematics or crack deformation. The work at hand presents cohesive fracture by elaborating phase‐field modeling within the RCE approach. It constitutes a classical traction‐separation exhibition at the crack faces of the RCE. As such, a phenomenological cohesive adhesion in the RCE can be modeled. In the sequel, the overall material status is interpolated by an intact material state (continuous description) and a fully broken state (RCE description) using the phase‐field degradation function. This allows not only to model a cohesive debonding failure for tensile and shearing deformation, but also to yield an expected contact algorithm when the crack is closing. Furthermore, the unknown crack deformations are solved according to virtual power principle, which provides a consistent framework for the comprehensive constitutive laws of this model.

3D cohesive fracture of heterogeneous CA-UHPC: A mesoscale investigation

Ultra high performance concrete with coarse aggregates (CA-UHPC) exhibits complicated damage and failure mechanisms due to intricate interactions of irregular mesoscale phases, including random aggregates, fibres, mortar, and interfaces. This work proposes a 3D numerical framework to investigate the complex cohesive fracture of CA-UHPC at mesoscale for the first time. Automatic algorithms are proposed to model realistic aggregates, mortar, aggregate-mortar interfaces and steel fibres in large quantities. Zero-thickness cohesive interface elements are automatically inserted in the mortar and on the aggregate surfaces to capture potential cracks, and an efficient non-conforming methodology is developed to model the fibre-mortar bond-slip behaviour using orientation-dependant pullout force-slip relations. The proposed models are validated using typical uniaxial tension tests, and elucidate that the progressive interactions of aggregate barrier, interfacial cracking and fibre bridging govern the early cracking, strain-hardening behaviour, fibre activation and final crack networks. Quantitative analyses are performed to optimize the mechanical properties of CA-UHPC: as the aggregate content increases, there are more torturous crack surfaces and fewer activated fibres with lower load-carrying capacities, but the downside of coarse aggregates can be alleviated by increasing fibre content, especially when needing aggregates to reduce carbon footprints and improve anti-shrinkage performance.

Effects of post-treatment on metal-ceramic bond properties of selective laser melted Co-Cr dental alloy. Part 1: Annealing temperature

Statement of problemDental cobalt-chromium (Co-Cr) alloy manufactured by selective laser melting (SLM) is not recommended for clinical applications before annealing because of excessive residual stress. However, limited information is available regarding the relationship between annealing temperature and the metal-ceramic bond properties of SLM Co-Cr alloys. PurposeThe purpose of this in vitro study was to investigate the effects of annealing temperature on the metal-ceramic bond properties of SLM Co-Cr alloys. Material and methodsFour groups with different annealing temperatures (850 °C; 950 °C; 1050 °C; 1150 °C) were prepared by using SLM techniques. Bond strengths were measured by using a 3-point bend test; subsequently, debonded surface morphologies and elements were assessed by using a scanning electron microscopy (SEM) coupled with energy-dispersive X-ray spectroscopy (EDS). The area fraction of adherence porcelain (AFAP) value was introduced to analyze fracture characteristics. Microstructural and interfacial characteristics were characterized by SEM/EDS and X-ray diffraction analysis. The coefficient of thermal expansion (CTE) test was used to analyze thermal matching. A 1-way ANOVA and the Tukey honestly significant difference tests were used to analyze bond strengths and AFAP values statistically (α=.05). ResultsThe mean ±standard deviation values of the metal-ceramic bond strengths were 40.68 ±4.34 MPa for the 850 °C group, 37.54 ±5.34 MPa for the 950 °C group, 45.97 ±2.18 MPa for the 1050 °C group, and 50.79 ±1.79 MPa for the 1150 °C group. Significant differences (P<.05) were observed among all groups. Debonded surfaces and AFAP analysis displayed a mixed fracture mode of adhesive and cohesive fracture, and 1150 °C-annealing specimens exhibited better fracture characteristics close to cohesive fractures. As the temperature increased, native oxide film thicknesses remained unchanged; the 850 °C group had the thinnest diffusion layer, while the other 3 groups had similar thicknesses. Although the 1050 °C and 1150 °C groups displayed higher CTE values, their microstructures were more conducive to atomic diffusion and improved chemical bonding. Microstructure analysis found that ε phase and second-phase precipitates jointly affected metal-ceramic bond strength. ConclusionsAnnealing temperatures affected the metal-ceramic bond strengths of SLM Co-Cr porcelain specimens. 1150 °C annealing SLM Co-Cr specimens displayed higher bond strengths and improved fracture and interface characteristics among the 4 groups.

A phase-field cohesive zone model for fracture simulation of asphalt mixture

The traditional cohesive zone model (CZM) based on interfacial damage mechanics has been widely used in quasi-brittle fracture simulation of asphalt mixture at low temperature. However, the traditional CZM is mesh dependent in the cohesive fracture simulation. This study aims to introduce a phase field method (PFM) to simulate brittle failure of asphalt mixture. The model was implemented in a framework of finite element method (FEM). The uniaxial tensile test was used to simulate the sensitivity of parameters that may affect the results. Furthermore, typical laboratory tests for evaluating the crack resistance of asphalt mixtures, such as the single-edge notched beam (SEB) test and the semi-circular bending (SCB) test, were simulated to validate the suitability of the PFM. Moreover, the numerical results and computational efficiency of the PFM-based cohesive fracture simulation within FAM was also discussed and compared with those based on CZM. The results indicate that the numerical results of the typical failure tests based on PFM are in good agreement with the experimental results at both macro and micro scales. In addition, the numerical results of cohesive fracture simulation within FAM based on PFM and CZM are slightly different. The brittle behavior of the asphalt mixture predicted based on PFM was more pronounced compared to the results predicted by CZM. Moreover, the cohesive fracture simulation based on PFM requires less computational memory and time. In general, this paper successfully introduced a PFM to study the quasi-brittle failure of asphalt mixture.

Study on the developmental characteristics and mechanism of shale FPZs

The fracture process and behavior of shale play a key role in the success of hydraulic fracturing stimulation in shale reservoirs. In this study, the central straight cracked Brazilian disc (CSCBD) splitting test in three fracture directions (arrester, divider, and short transverse) is conducted to reveal the propagation behavior and mechanism of closed symmetric fractures in laminated shales, with a focus on the fracture process zone (FPZ). The developmental characteristics and anisotropy of the FPZ near the crack tip of Mode I fracture of shale are identified and quantified based on the digital image correlation (DIC) method. By monitoring the crack tip opening displacement (CTOD) during the whole process, the critical CTOD, as one of the pivotal cohesive parameters, is obtained, and the development of the FPZ can be phased into three stages by CTOD evolution patterns. Based on double-K fracture criterion, the initiation fracture toughness and unstable fracture toughness of shale fractures at different laminar configurations are also analyzed. Additionally, the cohesive fracture model in the shale FPZ is derived based on the power function form using the energy release rate method.

Fatigue performance analysis of strength-graded zirconia polycrystals for monolithic three-unit implant-supported prostheses

The aim of this study was to evaluate the fatigue behavior of strength-graded zirconia polycrystals used as monolithic three-unit implant-supported prosthesis; complementarily, crystalline phase and micromorphology were also assessed. Fixed prostheses with 3 elements supported by 2 implants were confectioned, as follows: Group 3Y/5Y – monolithic structures of a graded 3Y-TZP/5Y-TZP zirconia (IPS e.max® ZirCAD PRIME); Group 4Y/5Y - monolithic structures of a graded 4Y-TZP/5Y-TZP zirconia (IPS e.max® ZirCAD MT Multi); Group Bilayer – framework of a 3Y-TZP zirconia (Zenostar T) veneered with porcelain (IPS e.max Ceram). The samples were tested for fatigue performance with step-stress analysis. The fatigue failure load (FFL), the number of cycles required until failure (CFF), and the survival rates in each cycle were recorded. The Weibull module was calculated and the fractography analyzed. The crystalline structural content via Micro-Raman spectroscopy and the crystalline grain size via Scanning Electron microscopy were also assessed for graded structures. Group 3Y/5Y showed the highest FFL, CFF, probability of survival, and reliability (based on Weibull modulus). Group 4Y/5Y showed significantly superior FFL and probability of survival than group bilayer. Fractographic analysis revealed catastrophic flaws in the monolithic structure and cohesive fracture of porcelain in bilayer prostheses, all originating from the occlusal contact point. The graded zirconia presented small grain size (≤0.61 μm), with the smallest values at the cervical region. The main composition of graded zirconia was of grains at tetragonal phase. The strength-graded monolithic zirconia, especially the 3Y-TZP/5Y-TZP, showed to be promising for use as monolithic three-unit implant-supported prosthesis.

Damage model for simulating cohesive fracture behavior of multi-phase composite materials

We propose a new damage model for simulating the cohesive fracture behavior of multi-phase composite materials such as concrete. The proposed model can evaluate the damage of the matrix-phase in composite materials using the volume fraction of the matrix within an element comprising the matrix and other materials. The damage model was first formulated for 1D problems and then extended to two-dimensional (2D) and three-dimensional (3D) problems using the equivalent strain based on the modified von-Mises criterion. The validity of the damage model was verified for 1D and 2D problems, and the model was also applied to the simulation of 3D cohesive crack growth in a heterogeneous solid with a large number of spherical inclusions. The results confirm that the proposed model allows the meshless finite element analysis of cohesive fracturing in composite materials.

DeepFEM: A Novel Element-Based Deep Learning Approach for Solving Nonlinear Partial Differential Equations in Computational Solid Mechanics

In this paper, an element-based deep learning approach named DeepFEM for solving nonlinear partial differential equations (PDEs) in solid mechanics is developed to reduce the number of sampling points required for training the deep neural network. Shape functions are introduced into deep learning to approximate the displacement field within the element. A general scheme for training the deep neural network based on derivatives computed from the shape functions is proposed. For the sake of demonstrations, the nonlinear vibration, nonlinear bending, and cohesive fracture problems are solved, and the results are compared with those from the existing methods to evaluate the performance of the present method. The results demonstrate that DeepFEM can effectively approximate the solution of the nonlinear mechanics problems with high accuracy, while the shape functions can significantly improve the computational efficiency. Moreover, with the trained DeepFEM model, the solutions of nonlinear problems with different geometric or material properties can be obtained instantly without retraining. Finally, the proposed DeepFEM is employed in the identification of material parameters of composite plate. The results show that the longitudinal and transverse elastic moduli of the ply in the composite plates can be accurately predicted based on the nonlinear mechanical response of plates.

Posterior Dahl: A Minimally Invasive Method for the Treatment of Localized Posterior Tooth Wear.

This retrospective case series of 9 patients aimed to describe clinical outcomes and patient satisfaction following the implementation of the posterior Dahl concept to manage localized posterior tooth wear. Localized occlusal space was created in the posterior dentition. Supra-occluding direct restorations were placed bilaterally for the restoration of molars. Intraoral scans were taken at the pre-treatment stage, immediately post-restoration, and during follow-up appointments. Scans were used to undertake analysis of any occlusal changes and re-establishment of the occlusion. A questionnaire was used to assess patient satisfaction, alleviation of any pre-treatment concerns, and evaluation of post-treatment complaints. Immediately post-treatment, all patients showed an increase in the vertical dimension. Opening of the bite in the untreated areas following restoration of worn posterior molars resulted either in a tendency towards or the actual reestablishment of the occlusion. One patient completely lacked compensatory vertical tooth movement in the untreated areas, culminating in the persistence of a vertical open bite. One restoration displayed cohesive fracture after 4 months. Pre-treatment problems (eg, sensitivity) were fully resolved amongst all patients after 6 months. Post-treatment complaints were minor and demonstrated resolution within a relatively short period of time. Eight patients reported being "very satisfied" with their treatment outcomes. Application of the posterior Dahl concept appears to offer a promising, relatively simple, minimally invasive and effective approach for the management of localized posterior tooth wear, which is well accepted by patients.

Virtual element method for mixed-mode cohesive fracture simulation with element split and domain integral

We present a computational framework for mixed-mode cohesive fracture simulation based on the virtual element method (VEM). To represent an arbitrary crack path, the element splitting scheme is developed on a polygonal mesh to capitalize its flexibility in element shape. For the accurate evaluation of a crack-tip stress field and crack propagation direction, the virtual grid-based stress recovery scheme is tailored for VEM in conjunction with the maximum strain energy release rate criterion. The mixed-mode fracture examples are illustrated to validate the accuracy and robustness of the proposed computational scheme. Numerical results demonstrate that the domain integral method with the stress recovery scheme captures an accurate crack path without oscillation under the biaxial tensile stress state. Furthermore, the computed cracks using the element splitting scheme show that smooth and curved patterns on polygonal elements are in good agreement with the experimental results.