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Mechanical damage to the meninges, which protect the spinal cord from blunt external forces, can cause idiopathic cerebrospinal fluid (CSF) leakage. This is probably because even a small meningeal failure leads to the leakage of CSF out of the subarachnoid space. However, the dura mater, the outermost layer of the meninges, is especially resilient and structurally tough. Moreover, CSF leakage can be caused by daily activities, including coughing, sneezing, and falling. Because of these contradicting facts, the essential mechanism of CSF leakage is difficult to understand. Recently, extensive efforts have been made to elucidate the mechanism of traumatic and impact-related injuries through computational simulations. It is crucial to comprehend the actual failure mode of biological materials under in vivo-like injurious loading conditions to enhance the accuracy of injury prediction. Therefore, in this study, we focused on the relationship between the intrinsic shape of wrinkles formed on the dural surface and the mechanical failure mode of the spinal dura mater. We found that a generated crack runs along the microscopic wrinkles in the longitudinal direction even when the spinal dura mater is statically pressurized.

In this paper the frictional heating effect on the propagation of surface crack under Hertzian contact loading based on the fracture mechanics is investigated. For the theoretical analysis of this effect, we estimated stress intensity factor of surface crack -tip in shear mode under Hertzian contact sliding friction. Theoretical results showed those thermal loads (Th), Peclet number (Pe) and crack angle (β) are very important factors on the propagation of surface crack under Hertzian contact loading. When thermal load(Th) and Peclet number(Pe) are constant, maximum variable range of stress intensity factor, ΔKII, is located in the range of surface crack angle 130°~150°. Non-dimensional parameter T consisting of thermal load and peclet number for evaluating ceramic wear behavior is introduced.

The durability and reliability of thermal barrier coatings(TBCs) have become a major concern of hot-section components due to lack of a reliable life prediction model. In this paper, it is found that the failure location of TBCs is at the TBC/TGO interface by a sequence of crack propagation and coalescence process. The critical crack length of failure samples is 8.8mm. The crack propagation rate is 3-10µm/cycle at the beginning and increases largely to 40µm/cycle near coating failure. A life prediction model based a simple fracture mechanics approach is proposed.

A modified single-edge notch tension (SENT) specimen exposed to saline environment was utilized to investigate the corrosion–fatigue crack growth behaviors of 5083, 6005 and 7N01 aluminum alloys. The fatigue crack propagation life, corrosion–fatigue crack rate ($da/dN$) were tested. The microstructures and fracture surfaces of specimens were examined by optical microscopy and scanning electron microscopy (SEM). The results showed that fatigue crack propagation rate of 7N01 in 3.5% NaCl was significantly higher than 6005 and 5083 alloys. The mechanisms of anodic dissolution and hydrogen embrittlement are used to explain the results.

This study investigates the crystallographic orientations most widely known to exhibit fractures in silicon, such as those on the (111) plane cracks travelling along the direction ( cracks). The (111) crack plane is believed to be the most stable fracture plane. However, fracture instabilities caused by brittle crack jumps remain on (111) the crack plane in a discontinuous manner. In this study, molecular dynamics simulations were performed to investigate the atomistic-level studies of fracture properties under a uniaxial tensile load (mode I load) in the (111) Si system. Our simulation results suggest that the formation of untypical-membered Si atomic rings in the vicinity of the crack tip, which can be induced by atomic stress near the crack tip, has an important role in the behavior of crack propagation instabilities. The presence of untypical-membered Si atomic rings acts as a self-protecting mechanism that contribute in maintaining the crack on the (111) fracture plane. Notably, our simulations also presented that the situation when a seven-Si atomic ring moves away from the crack tip associated with a sudden jump of crack speed can be regarded as the origin of the peculiar speed advancement behavior of the systems. Moreover, several of our simulation results are in agreement with related experimental measurements.

We study the lower semicontinuity for functionals of the form K → ∫_K φ (x, ν)dℋ¹ defined on compact sets in ℝ² with a finite number of connected components and finite ℋ¹ measure and apply the result to the study of quasi-static growth of brittle fractures in linearly elastic inhomogeneous and anisotropic bodies.

We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.⁹ The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L²-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Refs. 9 and 8, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith's criterion holds at the crack tips. We also prove that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough.

We propose a time-space discretization of a general notion of quasistatic growth of brittle fractures in elastic bodies proposed by Dal Maso, Francfort and Toader,¹⁴ which takes into account body forces and surface loads. We employ adaptive triangulations and prove convergence results for the total, elastic and surface energies. In the case in which the elastic energy is strictly convex, we also prove a convergence result for the deformations.

In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack need not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.

Coal failure behavior under dynamic loading is significant for dealing with the failure issues encountered in underground coal mines. In this study, the crack propagation and internal fracture process of coal under dynamic loading were investigated by a split Hopkinson pressure bar (SHPB) experimental system and numerical approach, respectively. The experimental and numerical results show that the coal crack propagation and internal fracture surface manifest significant multifractal features. Further, multifractal analysis suggests that the multifractal feature becomes more and more significant during the dynamic loading. The formation mechanism of the multifractal features was further discussed, and the result demonstrates that the crack propagation path within coal is essentially a multifractal structure, thus causing the total fracture behavior of coal to show multifractal features under dynamic loading. Moreover, the multifractal spectrum parameter $\mathrm{\Delta }{\alpha }_L$ was proved to be closely related to the brittle fracture property of coal, which transpires that the multifractal feature is feasible to evaluate the coal brittleness under dynamic loading and also applicable to predict the coal failure risk in underground coal mines.

In this study, the effect of contact pressure on fretting fatigue behavior of Al7075-T6 under cyclic normal contact loading is investigated. It is found that fretting fatigue life for the case of cyclic contact load was significantly less than that for constant contact load at the same axial and contact load levels, particularly for High Cycle Fatigue (HCF) conditions. The results showed that the fretting fatigue life decreased monotonically with the increase in normal contact load for all axial stresses. Examination of the fretting scars was performed using optical microscopy and numerical simulation was carried out using commercial finite element (FE) codes ABAQUS${}^{\text{®}}$ and FRANC2D/L${}^{{}^{\text{®}}}$ to calculate the crack propagation life. The crack initiation life was calculated by a combination of numerical and experimental results. Finally, the FE simulation was validated by a comparison between the numerical crack growth rate and the experimental measurement using replica.

Studies reveal that the most prominent cause of bearing failure is a crack on any of its mating surfaces. When the crack is initiated, the bearing can still be used for some duration, but this is majorly depending upon the loading conditions. This work primarily focuses on the effects of different levels of static loading on the crack propagation after crack initiation. To analyze the effect of static loading, an axial groove defect was seeded on the outer race of a taper roller bearing randomly and bearing run continuously under five different static loading conditions. Initially, the bearing was made to run under loading conditions to initiate the crack naturally but the crack was not initiated even after 800 h of running. Therefore, crack was initiated artificially for the purpose of studying crack propagation. It was observed from the experimentation that in the case of maximum static load of 20 kg, the crack propagates rapidly in terms of area after 109 h of continuous running, whereas in the case of no load, it started propagating quickly after 267.5 h of running. Statistical analysis was also carried out for the recorded signals at different intervals of times, and it was observed that the Shannon entropy value was showing a sudden rise with the edge breakage (visually verified) while the crack was propagating. However, in the statistical analysis, none of the parameters showed a correlation with crack propagation. To develop the correlation of crack propagation, Shannon entropy of high, medium and low frequency bands of continuous wavelet-based (CWT) was carried out using different wavelets. Shannon entropy for high frequency band of CWT using Daubechies 10 as mother wavelet has responded well to the crack propagation as the value showed a sudden rise and an overall increase for edge breakage and crack propagation, respectively. A high frequency band of CWT using Daubechies 10 was found suitable for detecting edge breakage and crack growth at the same time because of its capability to respond to transient characteristics for a large duration of time.

The girth welds of the steel connections in subsea pipelines are subjected to combined fatigue loading and static tensile loading in most of their service life. In this paper, both experimental and numerical studies are presented on the fatigue behavior of Carbon Fiber Reinforced Polymer (CFRP) composites repaired steel connections under combined loads. In the experimental program, each specimen is designed to be formed by two steel plates joined together by single-sided girth welds as a simplification of subsea pipelines, and reinforced by CFRP sheets on one side. The applied loads include a constant amplitude tensile cyclic load combined with a tensile static load, which is perpendicular to the cyclic load. The experimental results reveal that the superimposition of the tensile static load leads to a prolonged fatigue life. The effect gets more noticeable with increased tensile load. To further this study, an analytical model is developed on the basis of the Linear Elastic Fracture Mechanics (LEFM) method. It can be used to predict the fatigue lives efficiently. The comparisons with experimental results reveal that the analytical method is able to reasonably predict the fatigue crack growth life. Parametric studies are therefore performed using the proposed analytical model. The influence of CFRP layers, stress range and tensile static stress on the fatigue life was evaluated.

A layered rock mass is a special type of geological body. The existence of a bedding surface may lead to a poor cutting effect (over/under-excavation of the surrounding rock), falling of blocks, or collapse, thereby affecting most constructions in areas with such rocks. Given the lack of a proper quantitative analysis method for surrounding rock damages, the construction process of layered surrounding rock tunnels becomes difficult. To address these problems, three types of cut blasting models with single, double, and four holes are studied in this paper. With this, the LS-DYNA program is used to analyze the behaviors of stress wave propagation, crack propagation, and fracture modes, as well as fracture mechanisms of mudstone, sandstone, and layered rock. Using the image processing technology and fractal theory, the fractal dimension change trend and progressive damage evolution behavior of the three types of rocks under different cut blasting conditions are determined. Also determined is the corresponding relationship between the fractal dimension and the rock damage degree. The results indicate that crack initiation, propagation, bifurcation, and fractal dimension evolution are more closely related to the phenomenon where the compression wave is ahead of the tension wave, and the$\setminus$incompatible deformation of the bedding under single-hole blasting. Under double-hole and four-hole blasting, the phenomena, such as spalling, bedding crack penetration, and fracture connection between the explosive holes are caused mainly by the effects of stress concentration, reflected tension waves, and stress wave superposition. Moreover, under different blasting conditions, the rocks exhibit a similar progressive damage process, i.e. a rapid increase at first, then a slow rise, and finally a stabilization phase. The dynamic damage degree of the rock exhibits a linear increasing trend under different blasting holes. The study results provide a useful reference for blasting scheme design and optimization of underground engineering projects.

An enrichment technique for accurately modeling two dimensional crack propagation within the framework of the finite element method is presented. The technique uses an enriched basis that spans the asymptotic dynamic crack-tip solution. The enrichment functions and their spatial derivatives are able to exactly reproduce the asymptotic displacement field and strain field for a moving crack. The stress intensity factors for Mode I and Mode II are taken as additional degrees of freedom. An explicit time integration scheme is used to solve the resulting discrete equations. Numerical simulations of linear elastodynamic problems are reported to demonstrate the accuracy and potential of the technique.

As one type of rock slope failures, topping failure can be accurately simulated only when several aspects are correctly calculated such as deformation and stress, contacts between blocks, contact stress, movement of blocks, open/close of contacts between blocks, development of failure plane, and crack generation and propagation. Current numerical methods encounter many difficulties in simulating toppling failure, especially for rock slope with lots of rock-bridges. Numerical manifold method (NMM) can deal with these highly discontinuous problems and be used to model the toppling failure of rock slopes. This paper first introduces the fundamental principles, modeling of contacts, calculation of contact force and stress, and modeling of failure in NMM. Then, several case studies are conducted to testify the accuracy and convergence of method; comparisons with method, based on limit equilibrium principle, which was proposed by Goodman and Bray (G–B method) and centrifuge test are conducted. Finally, the topping failure of left bank of one high dam is simulated. Results show that the NMM can be used to correctly calculate the toppling safety factor, simulate the failure process of slope toppling, and accurately model the whole failure process of rock slopes with many rock-bridges.

Drill and blast method has been widely used as an effective excavation method for underground rock caverns or tunnels. To achieve a good blast design, an understanding on the rock dynamic response and rock fragmentation process is important. In this paper, numerical simulations are performed on a typical parallel hole cut blasting based on the discontinuous deformation analysis (DDA). The blast loading is obtained from the explicit FEM code LS-DYNA and the dynamic response of the rock mass is modeled by the DDA. Different influence factors on rock fragmentation under the blast loading are investigated, including the different delay time and various rock mass properties. Such a study will have potential applications for better drill and blast designs.

The twice-interpolation finite element method (TFEM) constructs the trial function for the Galerkin weak form through two stages of sequential interpolation without additional degrees of freedom and achieves better accuracy and convergence compared to the conventional finite element method (FEM). The TFEM has been shown to be insensitive to the quality of the elemental mesh and thus has the potential to simulate fracture problems. Intense examples and issues with cracking problems are investigated in this study. It is observed that the stress intense factor (SIF) of the crack tip can be evaluated with satisfactory accuracy. Since the present TFEM can produce more continuous nodal gradients, better stress fields can be reproduced, especially around the crack, without requiring more nodes. It is also shown that crack propagation can be reproduced readily and the cracking path agrees well with the reference solution and experimental results.

A new plane shape-free multi-node singular hybrid stress-function (HS-F) element with drilling degrees of freedom, which can accurately capture the stress intensity factors at the crack tips, is developed. Then, a quasi-static 2D crack propagation modeling strategy is established by combination of the new singular element and a shape-free 4-node HS-F plane element with drilling degrees of freedom proposed recently. Only simple remeshing with an unstructured mesh is needed for each simulation step. Numerical results show that the proposed scheme is an effective and robust technique for dealing with the crack propagation problems.

To investigate crack initiation and propagation of rock mass under coupled thermo-mechanical (TM) condition, a two-dimensional coupled TM model based on the numerical manifold method (NMM) is proposed, considering the effect of thermal damage on the rock physical properties and stress on the heat conductivity. Then, the NMM, using empirical strength criteria as the crack propagation critical criterion and physical cover as the minimum failure element, was extended for cracking process simulation. Furthermore, a high-order cover function was used to improve the calculation accuracy of stress. Therefore, the proposed method consists of three parts and has a high accuracy for simulating the cracking process in the rock mass under the coupled TM condition. The ability of the proposed model for high accuracy stress, crack propagation, and thermally-induced cracking simulation was verified by three examples. Finally, the proposed method was applied to simulate the stability of a hypothetical nuclear waste repository. Based on the outcome of this study, the application of NMM can be extended to study rock failure induced by multi-field coupling effect in geo-materials.