Normal Stress Distribution Research Articles

BEM analysis of protection of rock caverns from cracking by water infilling and rock softening

This paper studies the elastic behavior of near ground cavern infilled with water in a layered rock mass by applying axisymmetric boundary element method (BEM). The results of two case studies are presented to quantitatively show the effect of water infilling on the elastic stress and deformation of layered isotropic halfspaces with a spherical cavern. The cavern water pressure has a significant effect to the normal and shear stress distributions on the cavern surface. Moreover, the effect of water softening on the elastic modulus of the rock mass is considerable to the displacements on both the ground and cavern surfaces. However, this effect is insignificant for all induced stresses on the cavern surface. Hence, the full infilling of water in the rock cavern can protect the surrounding rock from cracking or fracturing because water softening can also increase the rock mass toughness.

Numerical investigations of joints with different surface roughness under shear and normal loads

A large number of discontinuities and weak planes exist in the natural system of rock masses. The presence of these discontinuities and weak planes reduces the strength of the rock masses. Thus, a thorough understanding of the shear behavior of jointed rocks is very important for many engineering projects. In this study, multistage normal loading (30, 60, 90, 180, and 360 kN) direct shear tests were conducted on a smooth planar joint using a large shear box device. Four numerical models with different joint asperities were built in parallel using Fast Lagrangian Analysis of Continua in three dimensions (FLAC3D), and the shear behavior was numerically analyzed. According to the experimental and numerical simulation results, joint roughness and normal force are the two most important factors that influence the shear behavior. The peak shear force increased as the normal load and joint asperity increased, but the normal displacement increased as the joint asperity increased and the normal load decreased. For the plane joint surface or joint surface with small asperity, the vertical displacement on the applied shear force side tended to go down, whereas it tended to go up on the opposite side. For the joint surface with large asperity, the vertical displacement on both sides went up. However, the value in the applied shear force side for the joint surface with large asperity was lower than that for the joint with smaller asperity. During shearing, the inclination of the upper box of the specimen is an important characteristic that causes the nonuniform distribution of normal stress, shear stress, and contact area of the interface. Furthermore, we developed a method for calculating the aperture size during shearing and discovered that the aperture size increased as the joint asperity increased. This research provides insight into the shear behavior of rock joints with various asperities.

Application of the four-dimensional lattice spring model in direct shear testing of intact rock

Rock shear strength and its influencing parameters, such as cohesion and friction angle, are critical for both surface and underground project rock engineering designs. The application of direct shear testing is more commonly employed for rock joints than for intact rock due to several limitations, such as the nonuniform normal stress distribution. Hence, triaxial tests are more frequently used to determine the cohesion and friction angle of intact rock specimens. However, compared to the basic tools of the direct shear test, these tests require more complex experimental equipment, making the triaxial testing less accessible to laboratories in general. Therefore, it is important to develop a method for making intact rock direct shear test results more accurate for engineering applications. To evaluate and enhance the accuracy of intact direct shear tests, laboratory experiments on intact cubic marble specimens and consequent numerical simulation were performed using the four-dimensional lattice spring model (4D-LSM). The 4D-LSM is arguably more efficient than the conventional discrete element method since it uses direct calibration of microscale parameters from macroscale parameters while maintaining the ability to reproduce material fracture. In this study, a two-stage simulation was introduced in the 4D-LSM to represent the stages when the normal and shear loads are applied. To determine the failure state of the specimen, the Mohr– Coulomb failure criterion was implemented into the 4D-LSM. A bilinear stiffness model was used to reproduce the shear force-displacement curve from the experiments. Our results show that this method was able to reproduce numerical results that are similar to those obtained in experimental direct shear tests.

Theoretical Analysis and Experimental Study on Normal Stress of Three Kinds of Beams Subjected to Pure Bending

The normal stresses of pure bending of a single rectangular cross-section beam, laminated beam and composite beam have been theoretically analyzed and calculated and experimentally tested by electrical measurement method in this paper. Through the analysis of the measured data, the correctness of theoretical calculations and experimental methods are verified, and the normal stress distribution laws of the three beams are revealed. The data shows that the normal stress of pure bending of the laminated beam is the largest, followed by that of the composite beam, and that of the single rectangular cross-section beam is the smallest. In addition, the reasons for the large errors of some experimental data are analyzed and discussed. By increasing the content and difficulty of the experiment, it is conducive to promote students to master more knowledge of material mechanics and exercise their practical skills. The result can provide a reference for the experimental teaching of material mechanics in other colleges and universities.

Biomechanical analysis of rigid and non-rigid connection with implant abutment designs for tooth-implant supported prosthesis: A finite element analysis

Background/purposeThe design of the connectors and implant abutments could affect the stress distribution of the tooth-implant supported prosthesis (TISP) entire system after loading. Therefore, the purpose of this study was to investigate the stress distribution of the TISP in different connectors and different implant abutments after loading. Materials and methodsThe TISP design used in this study was divided into six models. R1, R2 and R3 represented the tooth and the one-piece, two-piece and three-piece abutment implant system connected by a rigid connector, respectively, while NR1, NR2 and NR3 were the corresponding tooth-abutment implant systems connected by a non-rigid connector. A vertical occlusal load of 50 N was applied at a right angle on the 6 occlusal points of the occlusal surface. ResultsAs a result, regarding the maximum average stress distribution, R1 and NR1 appeared on the implant fixture, and the other four models were on the implant abutment. On the other hand, regardless of the abutment implant system, the maximum von Mises stress generated by the rigid connector was greater than the corresponding non-rigid connector in the cortical bone around implant. In addition, the three-piece abutment implant system had lower von Mises stress than the one-piece and two-piece implant systems in the cortical bone. ConclusionIt is concluded that by adding a flexible non-rigid connector and three-piece abutment device design to TISP, the occlusal load of the implant was dispersed, and the stress could be gradually introduced into the relatively strong implant abutment.

Mechanical model for the calculation of stress distribution on fault surface during the underground coal seam mining

The instability caused by the fault slip is one of the main factors that induce the occurrence of coal bursts. To in-depth understand the mechanisms responsible for coal bursts during the underground coal seam mining, a mechanical model used to calculate the stress distribution on fault surface and illustrate the fault slip characteristics is proposed by considering the mining-induced stress. In order to verify the validity of this model, a set of comparative analyses with experimental results which have been published in the previous studies are carried out. The results show that the normal and shear stress distribution on the fault surface calculated by the mechanical model is approximately consistent with the experimental stress results. According to the calculated stress distribution on the fault surface, normal and reverse faults formation mechanism are explained by this mechanical model when the lateral pressure coefficient is greater than 1.0 and less than 1.0. Meanwhile, fault potential energy is proposed to research the energy storage and further explain the mechanism of fault slip. In addition, the coal bursts occurrence induced by fault slip is also discussed according to the engineering background and this mechanical model.

Axisymmetric thermoelastic deformation of a multilayer plate with imperfect thermal contact of its layers

An axisymmetric stationary problem of thermoelasticity for a multilayer plate with imperfect thermal contact between its layers is solved by using the method of compliance functions along with the Hankel transform. It is assumed that the conditions of perfect mechanical contact are satisfied on their common boundaries. The Hankel transforms of displacements, stresses, and temperature at the points of the layer can be represented in the form of the linear combinations of the six auxiliary functions. The auxiliary functions are connected with the Hankel transforms of displacements, stresses, temperature and flow at the points of the upper boundary of the corresponding layer. For the problem considered six auxiliary functions can be found from the boundary conditions. Using the conditions on the common boundaries of the layers and entering a dummy layer the recurrent formulas for finding other auxiliary functions are constructed. The auxiliary functions of each layer are dependence. This dependence is represented in the matrix form using so-called compliance functions. The recurrence relations for the compliance functions of the thermoelastic multilayer plate are constructed. The algorithm for solving the сonsidered problem is formulated. The numerical calculations are made for a two-layer plate subjected to the action of the thermal loads. The influence of the coefficient of thermal resistance on the distribution of temperature at the points of the lower boundary of the upper layer and at the points of the upper boundary of the lower layer is analyzed. Also the influence of this coefficient on the distribution of normal stresses at the common boundary of layers is analyzed.

Super-resolving material microstructure image via deep learning for microstructure characterization and mechanical behavior analysis

The digitized format of microstructures, or digital microstructures, plays a crucial role in modern-day materials research. Unfortunately, the acquisition of digital microstructures through experimental means can be unsuccessful in delivering sufficient resolution that is necessary to capture all relevant geometric features of the microstructures. The resolution-sensitive microstructural features overlooked due to insufficient resolution may limit one’s ability to conduct a thorough microstructure characterization and material behavior analysis such as mechanical analysis based on numerical modeling. Here, a highly efficient super-resolution imaging based on deep learning is developed using a deep super-resolution residual network to super-resolved low-resolution (LR) microstructure data for microstructure characterization and finite element (FE) mechanical analysis. Microstructure characterization and FE model based mechanical analysis using the super-resolved microstructure data not only proved to be as accurate as those based on high-resolution (HR) data but also provided insights on local microstructural features such as grain boundary normal and local stress distribution, which can be only partially considered or entirely disregarded in LR data-based analysis.

Numerical simulations for studying the influence of friction in forging

ABSTRACT The modelling and simulation of forging has reached a matured stage, but the friction and friction models got only scant attention; this work intends to fill up that gap. Here, arbitrary Lagrangian-Eulerian (ALE) finite element method (FEM)-based numerical simulations are carried out for the forging of aluminium workpiece by considering two friction models – Coulomb-Siebel and Tresca. A relation between Coulomb’s coefficient of friction and friction factor has been established based on the slab method. The forging load is obtained by calculating the reaction force on the die as well as from energy method. Energy method provides more accurate and consistent results. Forging load and bulge increase with the friction, but at high friction, the effect is minimal. Bulge is found to be more sensitive to friction than the forging load. The distribution of normal stress is quite different on the die-workpiece interface compared to that on a parallel plane in the interior. The phenomenon of fold-over observed at high friction and high reduction observed in a Lagrangian formulation is absent in ALE formulation. The fold-over phenomenon occurs due to mesh distortion. It is not observed in a workpiece with round corners, even while using Lagrangian formulation.

DFT study of silicene on metal (Al, Ag, Au) substrates of various thicknesses

The silicene obtained on silver and gold substrates is not a subject for a large-scale use due to the high cost of the substrate materials. The aim of this work is to find a suitable low-cost substrate for the bulk production of silicene. In this work, three materials were investigated as a silicene substrate: Al, Ag, and Au. In all these cases, a metallic type of electronic conductivity was established in the silicene/substrate system. It turned out that the aluminum substrate provides an even better adhesion to silicene than the gold one. Silicene on the Al (111) substrate demonstrates the most uniform distribution of normal stresses with a minimum value of local bursts. Thus, aluminum seems to be quite a competitive material for the silicene production. The main obstacle in using aluminum substrates for the silicene production is strong oxidation in air.

Study of the interaction of concrete walls with the foundation structure

This article presents a study of the factors that influence the mechanism of soil-structure interaction with a pilot building having concrete walls and their impact on their performance. To illustrate the studies carried out, a numerical modeling of a four-floor concrete wall pilot building was performed, subjected to vertical actions, supported by a slab-on-ground foundation, using the Finite Element Method (FEM), together with specific 3D software for analysis and structural dimensioning in reinforced concrete. For the consideration of the geotechnical and structural system (foundation structure), the discrete spring model (Winkler model) coupled to the superstructure was used and the slab foundation thickness was varied by 16 cm, 25 cm and 40 cm. The local geotechnical formation was represented by a soft clay (SPT = 5) from the Belo Horizonte Metropolitan Region, Brazil. The influential factors of the SSI analyzed in this research were: relative stiffness of the foundation structure, requesting stresses, settlements in the foundation of the building and steel reinforcement bar ratio. For a better visualization of the influence of these various factors, an analysis was made of the distribution of normal stresses and stresses at the base of the walls of this building, in the form of graphs. Finally, it was concluded that the change in slab foundation, stiffness influences the distribution of stresses and stresses in the foundation, with a tendency to uniformity as the slab foundation thickness increases. However, this relationship is not linear.

Influence of Shear Heating and Thermomechanical Coupling on Earthquake Sequences and the Brittle‐Ductile Transition

AbstractLocalized frictional sliding on faults in the continental crust transitions at depth to distributed deformation in viscous shear zones. This brittle‐ductile transition (BDT), and/or the transition from velocity‐weakening (VW) to velocity‐strengthening (VS) friction, are controlled by the lithospheric thermal structure and composition. Here, we investigate these transitions, and their effect on the depth extent of earthquakes, using 2D antiplane shear simulations of a strike‐slip fault with rate‐and‐state friction. The off‐fault material is viscoelastic, with temperature‐dependent dislocation creep. We solve the heat equation for temperature, accounting for frictional and viscous shear heating that creates a thermal anomaly relative to the ambient geotherm which reduces viscosity and facilitates viscous flow. We explore several geotherms and effective normal stress distributions (by changing pore pressure), quantifying the thermal anomaly, seismic and aseismic slip, and the transition from frictional sliding to viscous flow. The thermal anomaly can reach several hundred degrees below the seismogenic zone in models with hydrostatic pressure but is smaller for higher pressure (and these high‐pressure models are most consistent with San Andreas Fault heat flow constraints). Shear heating raises the BDT, sometimes to where it limits rupture depth rather than the frictional VW‐to‐VS transition. Our thermomechanical modeling framework can be used to evaluate lithospheric rheology and thermal models through predictions of earthquake ruptures, postseismic and interseismic crustal deformation, heat flow, and the geological structures that reflect the complex deformation beneath faults.

Normal stress distribution of timber-concrete composite panels with an adhesive shear connection under thermal and humidity loadings

Humidity and temperature conditions have a substantial influence on the stresses and total deformation of timber-concrete composite panels, especially in terms of the high rigidity of the shear connection. In the present research, the normal stresses that resulted from the hygrothermal load of timber-concrete composite panels with an adhesive shear connection were analyzed. Three timber-concrete composite panel specimens were placed in controlled climate conditions. Strains in two orthogonal directions were measured. The stress distribution resulted from an approximate analytical calculation model. The results show that the highest stresses occurred near the shear connection. An increase in timber moisture content by 2.1% was predicted to result in exceeding the flexural tensile strength in the concrete perpendicular to the timber grain direction. At an outdoor temperature range, stresses influenced only by the temperature alone will possibly not cause a failure of timber or concrete. Under winter environmental conditions, the stress in timber can possibly reach 12% of the bending strength of the timber used.

Investigation on cutting resistance characteristic of bucket wheel excavator using DEM and DOE methods

As an important design parameter for bucket wheel excavator, the cutting resistance of the bucket wheel shows significant dynamic character and changes drastically under different work conditions. Therefore, this paper analyzes the trend of cutting resistance through a combination of discrete element method (DEM) and design of experiment (DOE). Firstly, the three-dimensional dynamic simulation of tool-particle cutting process is established using DEM. The accuracy of the DEM model is verified by the cutting resistance test. Based on DEM results, the cutting resistance, different flow regions and the contact normal stress distribution on the inside of the bucket were analyzed. Secondly, DOE method was used to analyze the changing regularity of the cutting resistance. With cutting speed, cohesion and particle size as variables, a total of 15 orthogonal working conditions were designed and simulated through DEM. Then, the response surface (RS) method is used to fit the original simulation results. The RS fitted results show that: (1) overall, the cutting resistance decreases as the particle size and cutting speed increase. A larger particle size will reduce the load weight of a single bucket by reducing the particle volume fraction, while a higher cutting speed will cause more particles to splash out of the bucket; (2) depending on different working conditions, the increasing of cohesion is able to increase the cutting resistance by increasing the cohesive force between particles, or reduce the cutting resistance through “big aggregates effect” which lowers the particle volume fraction.

Characterizing the Distribution of Temperature and Normal Stress on Flash Heated Granite Surfaces at Seismic Slip Rates

AbstractAt seismic slip rates, flash‐weakening can significantly reduce the coefficient of friction, and the magnitude of weakening increases with surface temperature. To quantify the distribution of flash temperature, high‐speed double‐direct shear experiments were conducted on Westerly granite blocks using velocity steps from 1 mm/s to 900 mm/s at 9 MPa normal stress. We employed a high‐speed infrared camera to measure surface temperatures on the moving block during sliding, and utilized a novel sliding‐surface geometry to control the mm‐scale contact history. Following the initial weakening upon the velocity step, the blocks slide at a constant coefficient of friction. Surface temperatures are inhomogeneously distributed across the sliding surface, and increase with displacement. To determine the local normal stress distribution at the mm‐scale, we combine a one‐dimensional thermal model with conventional flash‐weakening models that incorporate a surface temperature‐dependence informed by the controlled, mm‐scale contact history. Early contacts experience local normal stress exceeding 40 times the applied normal stress. As sliding progresses, the local normal stress at the hottest contacts decreases as contact area increases, leading to local normal stresses ranging from 2 to 6 times the applied normal stress on most contacts by 30 mm of slip. Increases in surface temperature, which would decrease the coefficient of friction, are buffered by wear processes that increase contact area and decrease the local normal stress. Treatments of flash heating are advanced by incorporating improved characterization of the state of the sliding surface at the mm and larger scales during sliding.

Experiments and finite element analysis for detecting the embedded defects in concrete using PZT transducers

Deficiencies inside concrete may reduce the load-bearing capacity and bring potential safety and durability problems to infrastructures. Detection of concrete deficiencies at the earliest time poses a great importance on structure safety. While there is still a lack of accurate and efficient method for quantitative evaluation of defects in concrete structures. In this study, the damage index was introduced to quantitatively evaluate the defects in concrete using piezoelectric (PZT) transducers. Meanwhile, the simulations of transducer excitation, the wave propagation in concrete, and the transducer receiving were established by Abaqus software. The results indicate that the localization and quantitative evaluation of defects in concrete could be achieved by using the damage index. The relative deviation of wave velocity and amplitude between the numerical and experimental results was within 15% and 20% respectively. The change of damage index obtained from experiments could be reasonably explained by the changing of normal stress distribution of finite element analysis. Numerical modeling could also help to understand and analyze the ultrasonic signal attenuation of the experimental results by using the normal stress distribution along propagation path.

Investigation on large elastoplastic deformation in expansion and springback for a composited bioresorbable stent

Mechanical performances for a composited bioresorbable stent were investigated by using the finite element method, which concerns the elastoplastic large deformation of expansion and springback during stent implantation. The introduced stent is composited by the outer layer of poly-L-lactic acid (PLLA) and the core of magnesium alloy (Mg alloy). As comparisons, meanwhile two single-material stents of PLLA and Mg alloy with the same geometric structures as the composited stent were considered. The numeric simulation results indicated that, the wrapping of PLLA can make the maximum Mises stress locate at the interior, it is beneficial to slow down the earlier surface degradation of stents caused by stress concentration. Also, the variation of residual deformation and stress distribution in Mg alloy core after PLLA outer layer degraded entirely are analyzed. The distributions of normal and total shear stresses on the interface of two materials were also calculated for the cases of expansion and springback. In addition, the analysis reveals the radius of implanted stent is in approximate linearly related to the expansion displacement load.

Laboratory hydraulic stimulation experiments to investigate the interaction between newly formed and preexisting fractures

Hydraulic stimulation in an enhanced geothermal reservoir (EGS) often creates a complex fracture network. It is understood that a fracture network includes both preexisting natural fractures and newly formed fractures. Analyzing the interaction between preexisting fractures and newly formed fractures during hydraulic stimulation is thus necessary to better understand the creation of a fracture network.In this study, we conducted laboratory scale hydraulic fracturing experiments to investigate how a fracture network is created when a propagating hydraulic fracture and a preexisting fracture interact. We observed that a secondary fracture (wing crack) was initiated and propagated from the tip of one side of a slipping preexisting fracture when a propagating hydraulic fracture follows the preexisting fracture. The laboratory experiments were analyzed by a numerical model that fully couples fluid flow between fracture surfaces and fracture deformations. The numerical analysis shows that the stress field induced by an upstream hydraulic fracture causes asymmetric distributions of normal and shear stresses along the preexisting fracture when they intersect, which resulted in initiation of a wing crack from the fracture tip on the side with larger angles. If a preexisting fracture is sufficiently large so that those tips are far from the strong effect of stress shadowing by an upstream fracture, it is possible that wing cracks propagate from both tips of the preexisting fracture. The wing cracks observed in the experiments are an important factor in improving reservoir permeability in an EGS reservoir because it has been observed in the field that secondary fractures that form as a result of fault slip can link originally discontinuous faults and enhance hydraulic conductivity underground. This type of reservoir permeability enhancement may be expected to occur by hydraulic stimulation because slipping preexisting fractures are better connected to one another by the formation of wing cracks.

Application of Spectral Method for Vibration-Induced High-Cycle Fatigue Evaluation of an High-Pressure Turbine Blade

Abstract A method of fluid–structure interaction coupling is implemented for a forced-response, vibration-induced fatigue life estimation of a high-pressure turbine blade. Two simulations approaches; a two-way (fully coupled) and one-way (uncoupled) methods are implemented to investigate the influence of fluid–solid coupling on a turbine blade structural response. The fatigue analysis is performed using the frequency domain spectral moments estimated from the response power spectral density (PSD) of the two simulation cases. The method is demonstrated in relation to the time-domain method of the rainflow cycle counting method with mean stress correction. Correspondingly, the mean stress and multi-axiality effects are also accounted for in the frequency domain spectral approach. In this case, a multiplication coefficient is derived based on the Morrow equation, while the case of multi-axiality is based on a criterion which reduces the triaxial stress state to an equivalent uniaxial stress using the critical plane assumption. The analyses show that while the vibration-induced stress histories of both simulation approaches are stationary, they violate the assumption of normality of the frequency domain approaches. The stress history profile of both processes can be described as platykurtic with the distributions having less mass near its mean and in the tail region, as compared to a Gaussian distribution with an equal standard deviation. The fully coupled method is right leaning with positive skewness while the uncoupled approach is left leaning with negative skewness. The directional orientation of the principal axes was also analyzed based on the Euler angle estimation. Although noticeable differences were found in the peak distribution of the normal stresses for both methods, the predicted Euler angle orientations were consistent in both cases, depicting a similar orientation of the critical plane during a crack initiation and propagation process. Finally, the fatigue life estimation was shown to be conservative in the fully coupled solution approach.

Numerical Simulation of a 2D Layered Anode for use in Lithium-Ion Batteries

An important technological problem is solved by numerical methods. Doping of silicene with phosphorus allows changing the morphology of the walls of the silicene channel without reducing their strength. The structure of lithium packings in the channels is studied in detail. The distribution of normal stresses in the walls of the channel before lithium intercalation and after complete lithium filling is determined. The calculated densities of electronic states allow us to conclude that both doped and undoped silicene on a graphite substrate become electrically conductive. The studied two-dimensional silicene can be used as an anode for next-generation lithium-ion batteries.