Finite element modeling of frictional contact and stress intensity factors in three-dimensional fractured media using unstructured tetrahedral meshes

This thesis introduces a three-dimensional (3D) finite element (FE) formulation to model the linear elastic deformation of fractured media under tensile and compressive loadings. The FE model is based on unstructured meshes using quadratic tetrahedral elements, and includes several novel components: (i) The singular stress field near the crack front is modeled using quarter-point tetrahedral finite elements. (ii) The frictional contact between the crack faces is modeled using isoparametric contact discretization and a gap-based augmented Lagrangian method. (iii) Accurate stress intensity factors (SIFs) of 3D cracks computed using the two novel approaches of displacement correlation and disk-shaped domain integral. The main contributions in the FE modeling of 3D cracks are: (i) It is mathematically proven that quarter-point tetrahedral finite elements (QPTs) reproduce the square root strain singularity of crack problems. (ii) A displacement correlation (DC) scheme is proposed in combination with QPTs to compute SIFs from unstructured meshes. (iii) A novel domain integral approach is introduced for the accurate computation of the pointwise $J$-integral and the SIFs using tetrahedral elements. The main contributions in the contact algorithm are: (i) A square root singular variation of the penalty parameter near the crack front is proposed to accurately model the contact tractions near the crack front. (ii) A gap-based augmented Lagrangian algorithm is introduced for updating the contact forces obtained from the penalty method to more accurate estimates. The results of contact and stress intensity factors are validated for several numerical examples of cubes containing single and multiple cracks. Finally, two applications of this numerical methodology are discussed: (i) Understanding the hysteretic behavior in rock deformation; and (ii) Simulating 3D brittle crack growth. The results in this thesis provide significant evidence that tetrahedral elements are efficient, reliable and robust instruments for accurate linear elastic fracture mechanics calculations.Open Acces

Highly selective and sensitive determination of copper ion by two novel optical sensors

AbstractNew optical sensors for the determination of copper ion by incorporation of 1,1′-(4-nitro-1,2-phenylene)bis(azan-1-yl-1-ylidene)bis(methan-1-yl-1-lidene)dinaphthalen-2-ol(L1), 1,1′-2,2′-(1,2-phenylene)bis(ethene-2,1-diyl)dinaphthalen-2-ol 1(L2), dibutylphthalate (DBP) and sodium tetraphenylborate (Na-TPB) to the plasticized polyvinyl chloride matrices were prepared. The tendency of both ionophores (L2 and L1) as chromoionophore was significantly enhanced by the addition of DBP to the membrane. The proposed sensors benefit from advantages such as high stability, reproducibility and relatively long lifetime, good selectivity for Cu2+ ion determination over a large number of alkali, alkaline earth, transition and heavy metal ions. At optimum values of membrane compositions and experimental conditions, both sensors’ response was linear over a concentration range of 7.98×10−6 to 1.31×10−4molL−1 and 1.99×10−6 to 5.12×10−5molL−1 for L2 and L1, respectively. Sensor detection limit based on the definition that the concentration of the sample leads to a signal equal to the blank signal plus three times of its standard deviation was found to be 3.99×10−7 and 5.88×10−7molL−1 for L2 and L1, respectively. The response time of the optodes (defined as the time required reaching the 90% of the peak signal) was found to be 5–8min for L2 and 20–25min for L1 based sensor. The proposed optical sensors were applied successfully for the determination of Cu2+ ion content in water samples

Comparison of Stresses Induced by Fiber Post, Parapost and Casting Post in Root Canals by Photoelasticity Method

INTRODUCTION: Many studies have been performed to evaluate the stress distribution around endodontic posts; those which compared posts composed of different materials are rare. The aim of this study was to compare stresses induced in dentin by three structurally different posts using photoelasticity method. MATERIALS AND METHODS: Nine blocks of PSM-5 Photoelastic material with 45×45×10 mm dimension were prepared. In each block, a canal 9 mm in length and 0.8 mm in width was drilled. Blocks were divided into 3 groups of three each. In the first group, the canals were prepared for insertion of Fiber Post with 1.25 mm width. In the second group, the canals were prepared for insertion of ParaPost with 1.25 mm width and the canals in the third group were prepared for casting post similar to the above samples. Casting Post pattern was made by Duralay resin and casted by Ni-Cr alloy. All posts were cemented in canals with Panavia cement. The stresses were evaluated in the polariscope under three different conditions: 1) without load, 2) with 135 N vertical load, and 3) with 90 N oblique load (26° inclination to post long axis). The fringe orders in the cervical, middle and apical regions of the posts were evaluated and compared with each other.RESULTS: Application of the vertical load induced a high stress concentration (FO=4) in the apical region of the ParaPost, while lower stress was observed in the middle (FO=2) and cervical region (FO=2+). Fiber Post and Casting Post showed even stress distribution (FO=2+). High stress concentration was detected with the application of oblique force in the cervical region of ParaPost (FO=5) and Casting Post (FO=3+). Fiber Posts fractured before reaching 90-N loading force. CONCLUSION: The stress distribution around Fiber Post and Casting Post were constant in comparison with ParaPost. Fiber Post with 1.25 mm width was not recommended in situations with high oblique stresses

The global burden of cancer attributable to risk factors, 2010-19 : a systematic analysis for the Global Burden of Disease Study 2019

Background Understanding the magnitude of cancer burden attributable to potentially modifiable risk factors is crucial for development of effective prevention and mitigation strategies. We analysed results from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019 to inform cancer control planning efforts globally. Methods The GBD 2019 comparative risk assessment framework was used to estimate cancer burden attributable to behavioural, environmental and occupational, and metabolic risk factors. A total of 82 risk-outcome pairs were included on the basis of the World Cancer Research Fund criteria. Estimated cancer deaths and disability-adjusted life-years (DALYs) in 2019 and change in these measures between 2010 and 2019 are presented. Findings Globally, in 2019, the risk factors included in this analysis accounted for 4.45 million (95% uncertainty interval 4.01-4.94) deaths and 105 million (95.0-116) DALYs for both sexes combined, representing 44.4% (41.3-48.4) of all cancer deaths and 42.0% (39.1-45.6) of all DALYs. There were 2.88 million (2.60-3.18) risk-attributable cancer deaths in males (50.6% [47.8-54.1] of all male cancer deaths) and 1.58 million (1.36-1.84) risk-attributable cancer deaths in females (36.3% [32.5-41.3] of all female cancer deaths). The leading risk factors at the most detailed level globally for risk-attributable cancer deaths and DALYs in 2019 for both sexes combined were smoking, followed by alcohol use and high BMI. Risk-attributable cancer burden varied by world region and Socio-demographic Index (SDI), with smoking, unsafe sex, and alcohol use being the three leading risk factors for risk-attributable cancer DALYs in low SDI locations in 2019, whereas DALYs in high SDI locations mirrored the top three global risk factor rankings. From 2010 to 2019, global risk-attributable cancer deaths increased by 20.4% (12.6-28.4) and DALYs by 16.8% (8.8-25.0), with the greatest percentage increase in metabolic risks (34.7% [27.9-42.8] and 33.3% [25.8-42.0]). Interpretation The leading risk factors contributing to global cancer burden in 2019 were behavioural, whereas metabolic risk factors saw the largest increases between 2010 and 2019. Reducing exposure to these modifiable risk factors would decrease cancer mortality and DALY rates worldwide, and policies should be tailored appropriately to local cancer risk factor burden. Copyright (C) 2022 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license.Peer reviewe

On the initiation of hydraulic fractures in anisotropic rocks

This paper addresses hydraulic fracture initiation from an initially notch-free wellbore situated in an anisotropic host rock, where the rock mass is subjected to an in-situ stress state that is also anisotropic in nature. In such conditions, hydraulic fracture initiation is fully characterized by three parameters, namely initiation pressure, initiation orientation, and initiation length. While a strength-based criterion captures only two of these parameters, break-down pressure and orientation, the evaluation of initiation length requires a mixed criterion approach in which both stress and energy conditions are met. We extend the existing mixed criterion formulation for isotropic rocks to also include anisotropic material behavior. We then investigate how material anisotropy interacts with stress anisotropy to determine the break-down pressure as well as the size and orientation of the starter crack. The results show that material anisotropy can overshadow the stress anisotropy, in the sense that it can drive the crack towards the weakest plane. It is demonstrated from a fracture energy perspective that the initiation length cannot extend as large as the fracture process zone length even when the wellbore size is unrealistically large. The difference between initiation pressures predicted by the mixed criterion and strength-based theory rises as the wellbore size decreases. Based on these observations, applying the mixed criterion is essential especially in relatively small wellbores.ISSN:1365-1609ISSN:0148-9062ISSN:1873-454

A multi-phasic approach for estimating the Biot coefficient for Grimsel granite

This paper presents an alternative approach for estimating the Biot coefficient for the Grimsel granite, which appeals to the multi-phasic mineralogical composition of the rock. The modelling considers the transversely isotropic nature of the rock that is evident from both the visual appearance of the rock and determined from mechanical testing. Conventionally, estimation of the compressibility of the solid material is performed by fluid saturation of the pore space and pressurization. The drawback of this approach in terms of complicated experimentation and influences of the unsaturated pore space is alleviated by adopting the methods for estimating the solid material compressibility using developments in theories of multi-phase materials. The results of the proposed approach are compared with estimates available in the literature

Crack tip asymptotic field and K-dominant region for anisotropic semi-circular bend specimen

This study reports the coefficients of the crack tip asymptotic field for the semi-circular bend (SCB) specimen made of anisotropic rocks when subjected to pure mode loading. The finite element over-deterministic method is employed to determine the singular and higher order terms of the crack tip asymptotic field for a wide range of geometry and anisotropy parameters associated with the Mode I SCB test. These parameters are helpful when analysing the fracture path and failure mechanism of anisotropic rocks in cases where the process zone is large compared to the crack length. We also apply an energy-based criterion on the crack tip fields to evaluate the size of the K-dominant region as a function of geometry configuration and anisotropy. It is concluded that the ISRM-suggested size requirement for the SCB samples of rock can yield underestimated values of fracture toughness due to the constraints applied to the FPZ development