Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

Study of hydro-mechanical behaviours of rough rock fracture with shear dilatancy and asperities using shear-flow model

The geometric properties of fracture surfaces significantly influence shear-seepage in rock fractures,introducing complexities to fracture modelling.The present study focuses on the hydro-mechanical behaviours of rough rock fractures during shear-seepage processes to reveal how dilatancy and fracture asperities affect these phenomena.To achieve this,an improved shear-flow model(SFM)is proposed with the incorporation of dilatancy effect and asperities.In particular,shear dilatancy is accounted for in both the elastic and plastic stages,in contrast to some existing models that only consider it in the elastic stage.Depending on the computation approaches for the peak dilatancy angle,three different versions of the SFM are derived based on Mohr-Coulomb,joint roughness coefficient-joint compressive strength(JRC-JCS),and Grasselli’s theories.Notably,this is a new attempt that utilizes Grasselli’s model in shearseepage analysis.An advanced parameter optimization method is introduced to accurately determine model parameters,addressing the issue of local optima inherent in some conventional methods.Then,model performance is evaluated against existing experimental results.The findings demonstrate that the SFM effectively reproduces the shear-seepage characteristics of rock fracture across a wide range of stress levels.Further sensitivity analysis reveals how dilatancy and asperity affect hydraulic properties.The relation between hydro-mechanical properties(dilatancy displacement and hydraulic conductivity)and asperity parameters is analysed.Several profound understandings of the shear-seepage process are obtained by exploring the phenomenon under various conditions.

A statistical damage-based constitutive model for shearing of rock joints in brittle drop mode

Some rock joints exhibit significant brittleness,characterized by a sharp decrease in shear stress upon reaching the peak strength.However,existing models often fail to accurately represent this behavior and are encumbered by numerous parameters lacking clear mechanical significance.This study presents a new statistical damage constitutive model rooted in both damage mechanics and statistics,containing only three model parameters.The proposed model encompasses all stages of joint shearing,including the compaction stage,linear stage,plastic yielding stage,drop stage,strain softening stage,and residual strength stage.To derive the analytical expression of the constitutive model,three boundary conditions are introduced.Experimental data from both natural and artificial rock joints is utilized to validate the model,resulting in average absolute relative errors ranging from 3%to 8%.Moreover,a comparative analysis with established models illustrates that the proposed model captures stress drop and post-peak strain softening more effectively,with model parameters possessing clearer mechanical interpretations.Furthermore,parameter analysis is conducted to investigate the impacts of model parameters on the curves and unveil the relationship between these parameters and the mechanical properties of rock joints.Importantly,the proposed model is straightforward in form,and all model parameters can be obtained from direct shear tests,thus facilitating the utilization in numerical simulations.

Predicting hepatocellular carcinoma: A new non-invasive model based on shear wave elastography

BACKGROUND Integrating conventional ultrasound features with 2D shear wave elastography(2D-SWE)can potentially enhance preoperative hepatocellular carcinoma(HCC)predictions.AIM To develop a 2D-SWE-based predictive model for preoperative identification of HCC.METHODS A retrospective analysis of 884 patients who underwent liver resection and pathology evaluation from February 2021 to August 2023 was conducted at the Oriental Hepatobiliary Surgery Hospital.The patients were divided into the modeling group(n=720)and the control group(n=164).The study included conventional ultrasound,2D-SWE,and preoperative laboratory tests.Multiple logistic regression was used to identify independent predictive factors for RESULTS In the modeling group analysis,maximal elasticity(Emax)of tumors and their peripheries,platelet count,cirrhosis,and blood flow were independent risk indicators for malignancies.These factors yielded an area under the curve of 0.77(95%confidence interval:0.73-0.81)with 84%sensitivity and 61%specificity.The model demonstrated good calibration in both the construction and validation cohorts,as shown by the calibration graph and Hosmer-Lemeshow test(P=0.683 and P=0.658,respectively).Additionally,the mean elasticity(Emean)of the tumor periphery was identified as a risk factor for microvascular invasion(MVI)in malignant liver tumors(P=0.003).Patients receiving antiviral treatment differed significantly in platelet count(P=0.002),Emax of tumors(P=0.033),Emean of tumors(P=0.042),Emax at tumor periphery(P<0.001),and Emean at tumor periphery(P=0.003).CONCLUSION 2D-SWE’s hardness value serves as a valuable marker for enhancing the preoperative diagnosis of malignant liver lesions,correlating significantly with MVI and antiviral treatment efficacy.

Numerical Analysis on Magnetic-induced Shear Modulus of Magnetorheological Elastomers Based on Multi-chain Model

Based on the magnetic interaction energy, using derivative of the magnetic energy density, a model is proposed to compute the magnetic-induced shear modulus of magnetorheological elastomers. Taking into account the influences of particles in the same chain and the particles in all adjacent chains, the traditional magnetic dipole model of the magnetorheological elastomers is modified. The influence of the ratio of the distance etween adjacent chains to the distance between adjacent particles in a chain on the magnetic induced shear odulus is quantitatively studied. When the ratio is large, the multi-chain model is compatible with the single chain model, but when the ratio is small, the difference of the two models is significant and can not be neglected. Making certain the size of the columns and the distance between adjacent columns, after constructing the computational model of BCT structures, the mechanical property of the magnetorheological elastomers composed of columnar structures is analyzed. Results show that, conventional point dipole model has overrated the magnetic-induced shear modulus of the magnetorheological elastomers. From the point of increasing the magnetic-induced shear modulus, when the particle volume fraction is small, the chain-like structure exhibits better result than the columnar structure, but when the particle volume fraction is large,the columnar structure will be better.

Adiabatic shear sensitivity of ductile metal based on gradient-dependent JOHNSON-COOK model

Based on the expression proposed by WANG for the local plastic shear deformation distribution in the adiabatic shear band（ASB） using gradient-dependent plasticity,the effects of 10 parameters on the adiabatic shear sensitivity were studied.The experimental data for a flow line in the ASB obtained by LIAO and DUFFY were fitted by use of the curve-fitting least squares method and the proposed expression.The critical plastic shear strains corresponding to the onset of the ASB for Ti-6Al-4V were assessed at different assigned ASB widths.It is found that the proposed expression describes well the non-linear deformation characteristics of the flow line in the ASB.Some parameters in the JOHNSON-COOK model are back-calculated using different critical plastic shear strains.The adiabatic shear sensitivity decreases as initial static yield stress,work to heat conversion factor and strain-rate parameter decrease,which is opposite to the effects of density,heat capacity,ambient temperature and strain-hardening exponent.The present model can predict the ASB width evolution process.The predicted ASB width decreases with straining until a stable value is reached.The famous model proposed by DODD and BAI only can predict a final stable value.

Effects of constitutive parameters on adiabatic shear localization for ductile metal based on JOHNSON-COOK and gradient plasticity models

By using the widely used JOHNSON-COOK model and the gradient-dependent plasticity to consider microstructural effect beyond the occurrence of shear strain localization,the distributions of local plastic shear strain and deformation in adiabatic shear band(ASB)were analyzed.The peak local plastic shear strain is proportional to the average plastic shear strain,while it is inversely proportional to the critical plastic shear strain corresponding to the peak flow shear stress.The relative plastic shear deformation between the top and base of ASB depends on the thickness of ASB and the average plastic shear strain.A parametric study was carried out to study the influence of constitutive parameters on shear strain localization.Higher values of static shear strength and work to heat conversion factor lead to lower critical plastic shear strain so that the shear localization is more apparent at the same average plastic shear strain.Higher values of strain-hardening exponent,strain rate sensitive coefficient,melting point,thermal capacity and mass density result in higher critical plastic shear strain,leading to less apparent shear localization at the same average plastic shear strain.The strain rate sensitive coefficient has a minor influence on the critical plastic shear strain,the distributions of local plastic shear strain and deformation in ASB.The effect of strain-hardening modulus on the critical plastic shear strain is not monotonous.When the maximum critical plastic shear strain is reached,the least apparent shear localization occurs.

A new shear rheological model for a soft interlayer with varying water content

The rheological behavior of a soft interlayer is critical to understanding slope stability, which is closely related to the water content of the soft interlayer. This study used the soft interlayer of the Permian Maokou Formation in Southwest China as an example to perform ring shear creep tests with different water content amounts. The effect of water content on the creep properties of the soft interlayer was analyzed, and a new shear rheological model was established. This research produced several findings. First, the ring shear creep deformation of the soft interlayer samples varied with the water content and the maximum instantaneous shear strain increment occurred near the saturated water content. As the water content increased, the cumulative creep increment of the samples increased. Second, the water content significantly affected the long-term strength of the soft interlayer, which decreased with the increase of water content, exhibiting a negative linear correlation. Third, a constitutive equation for the new rheological model was derived, and through fitting of the ring shear creep test data, the validity and applicability of the constitutive equation were proven. This study has developed an important foundation for studying the long-term deformation characteristics of a soft interlayer with varying water content.

Mathematical Model and Experiment Validation of Fluid Torque by Shear Stress under Influence of Fluid Temperature in Hydro-viscous Clutch

The current design of hydro-viscous clutch（HVC） in tracked vehicle fan transmission mainly focuses on high-speed and high power. However, the fluid torque under the influence of fluid temperature can not be predicted accurately by conventional mathematical model or experimental research. In order to validate the fluid torque of HVC by taking the viscosity-temperature characteristic of fluid into account, the test rig is designed. The outlet oil temperature is measured and fitted with different rotation speed, oil film thickness, oil flow rate, and inlet oil temperature. Meanwhile, the film torque can be obtained. Based on Navier-Stokes equations and the continuity equation, the mathematical model of fluid torque is proposed in cylindrical coordinate. Iterative method is employed to solve the equations. The radial and tangential speed distribution, radial pressure distribution and theoretical flow rate are determined and analyzed. The models of equivalent radius and fluid torque of friction pairs are introduced. The experimental and theoretical results indicate that tangential speed distribution is mainly determined by the relative rotating speed between the friction plate and the separator disc. However, the radial speed distribution and pressure distribution are dominated by pressure difference at the lower rotating speed. The oil film fills the clearance and the film torque increases with increasing rotating speed. However, when the speed reaches a certain value, the centrifugal force will play an important role on the fluid distribution. The pressure is negative at the outer radius when inlet flow rate is less than theoretical flow, so the film starts to shrink which decreases the film torque sharply. The theoretical fluid torque has good agreement with the experimental data. This research proposes a new fluid torque mathematical model which may predict the film torque under the influence of temperature more accurately.

A new model for evaluating the dynamic shear strength of rocks based on laboratory test data for earthquake-resistant design

The dynamic shear strength of rocks is required for the earthquake-resistant design of nuclear power plants in Japan.This research aims to propose a mathematical model for estimating the dynamic strength and to validate the model.Two different types of specimens were prepared for the model validation,and the monotonic and cyclic loading tests were conducted to obtain the mathematical model parameters.Subsequently,multistep cyclic loading tests were performed,followed by simulations using the mathematical model.The test results demonstrated that the dynamic shear strength exceeded the static shear strength,which agreed with previous researches.Furthermore,the dynamic shear strength calculated using the mathematical model was generally consistent with that obtained from the experimental data.

Nonlinear shear behavior of rock joints using a linearized implementation of the Barton-Bandis model

Experiments on rock joint behaviors have shown that joint surface roughness is mobilized under shearing,inducing dilation and resulting in nonlinear joint shear strength and shear stress vs.shear displacement behaviors.The Barton-Bandis(B-B) joint model provides the most realistic prediction for the nonlinear shear behavior of rock joints.The B-B model accounts for asperity roughness and strength through the joint roughness coefficient(JRC) and joint wall compressive strength(JCS) parameters.Nevertheless,many computer codes for rock engineering analysis still use the constant shear strength parameters from the linear Mohr-Coulomb(M-C) model,which is only appropriate for smooth and non-dilatant joints.This limitation prevents fractured rock models from capturing the nonlinearity of joint shear behavior.To bridge the B-B and the M C models,this paper aims to provide a linearized implementation of the B-B model using a tangential technique to obtain the equivalent M-C parameters that can satisfy the nonlinear shear behavior of rock joints.These equivalent parameters,namely the equivalent peak cohesion,friction angle,and dilation angle,are then converted into their mobilized forms to account for the mobilization and degradation of JRC under shearing.The conversion is done by expressing JRC in the equivalent peak parameters as functions of joint shear displacement using proposed hyperbolic and logarithmic functions at the pre-and post-peak regions of shear displacement,respectively.Likewise,the pre-and post-peak joint shear stiffnesses are derived so that a complete shear stress-shear displacement relationship can be established.Verifications of the linearized implementation of the B-B model show that the shear stress-shear displacement curves,the dilation behavior,and the shear strength envelopes of rock joints are consistent with available experimental and numerical results.

DEM modeling of high shear wet granulation of a simple system

High shear wet granulation(HSWG) is one of the most poorly understood processes with known difficulties in optimization and scale up. The purpose of the current study is to develop a DEM model which can be applied under dynamic process conditions with high predictive capacity to improve process insight. The DEM model is used to predict agglomeration as a function of impeller speed and liquid addition rate in a high shear wet granulator. The DEM model tracks dynamic formation and breakage of liquid bridges between particles as liquid binder in the system is added, and corrects for the change in material properties as a function of the binder content.

An interface shear damage model of chromium coating/steel substrate under thermal erosion load

The Cr-plated coating inside a gun barrel can effectively improve the barrel’s erosion resistance and thus increase the service life.However,due to the cyclic thermal load caused by high-temperature gunpowder,micro-element damage tends to occur within the Cr coating/steel substrate interface,leading to a gradual deterioration in macro-mechanical properties for the material in the related region.In order to mimic this cyclic thermal load and,thereby,study the thermal erosion behavior of the Cr coating on the barrel’s inner wall,a laser emitter is utilized in the current study.With the help of in-situ tensile test and finite element simulation results,a shear stress distribution law of the Cr coating/steel substrate and a change law of the interface ultimate shear strength are identified.Studies have shown that the Cr coating/steel substrate interface’s ultimate shear strength has a significant weakening effect due to increasing temperature.In this study,the interfacial ultimate shear strength decreases from 2.57 GPa(no erosion)to 1.02 GPa(laser power is 160 W).The data from this experiment is employed to establish a Cr coating/steel substrate interface shear damage model.And this model is used to predict the flaking process of Cr coating by finite element method.The simulation results show that the increase of coating crack spacing and coating thickness will increase the service life of gun barrel.

Adiabatic shear localization evolution for steel based on the Johnson-Cook model and gradient-dependent plasticity

Gradient-dependent plasticity is introduced into the phenomenological Johnson-Cook model to study the effects of strainhardening, strain rate sensitivity, thermal-softening, and microstructure. The microstructural effect （interactions and interplay among microstructures） due to heterogeneity of texture plays an important role in the process of development or evolution of an adiabatic shear band with a certain thickness depending on the grain diameter. The distributed plastic shear strain and deformation in the shear band are derived and depend on the critical plastic shear strain corresponding to the peak flow shear stress, the coordinate or position, the internal length parameter, and the average plastic shear strain or the flow shear stress. The critical plastic shear strain, the distributed plastic shear strain, and deformation in the shear band are numerically predicted for a kind of steel deformed at a constant shear strain rate. Beyond the peak shear stress, the local plastic shear strain in the shear band is highly nonuniform and the local plastic shear deformation in the band is highly nonlinear. Shear localization is more apparent with the increase of the average plastic shear strain. The calculated distributions of the local plastic shear strain and deformation agree with the previous numerical and experimental results.

Adiabatic Shear Localization for Steels Based on Johnson-Cook Model and Second-and Fourth-Order Gradient Plasticity Models

To consider the effects of the interactions and interplay among microstructures, gradient-dependent models of second- and fourth-order are included in the widely used phenomenological Johnson-Cook model where the effects of strain-hardening, strain rate sensitivity, and thermal-softening are successfully described. The various parameters for 1006 steel, 4340 steel and S-7 tool steel are assigned. The distributions and evolutions of the local plastic shear strain and deformation in adiabatic shear band （ASB） are predicted. The calculated results of the second- and fourth- order gradient plasticity models are compared. S-7 tool steel possesses the steepest profile of local plastic shear strain in ASB, whereas 1006 steel has the least profile. The peak local plastic shear strain in ASB for S-7 tool steel is slightly higher than that for 4340 steel and is higher than that for 1006 steel. The extent of the nonlinear distribution of the local plastic shear deformation in ASB is more apparent for the S-7 tool steel, whereas it is the least apparent for 1006 steel. In fourth-order gradient plasticity model, the profile of the local plastic shear strain in the middle of ASB has a pronounced plateau whose width decreases with increasing average plastic shear strain, leading to a shrink of the portion of linear distribution of the profile of the local plastic shear deformation. When compared with the sec- ond-order gradient plasticity model, the fourth-order gradient plasticity model shows a lower peak local plastic shear strain in ASB and a higher magnitude of plastic shear deformation at the top or base of ASB, which is due to wider ASB. The present numerical results of the second- and fourth-order gradient plasticity models are consistent with the previous numerical and experimental results at least qualitatively.

A five-parameter constitutive model for hysteresis shearing and energy dissipation of rock joints

Rock joints exhibit hysteresis shearing behavior and produce energy dissipation under shear cyclic loads,which however cannot be accurately depicted by existing constitutive models. This paper establishes a constitutive model for hysteresis shearing and associated energy dissipation of rock joints. Analytical expressions of the model during cyclic shearing processes are derived. Derivation of the model indicates no energy dissipation in the elastic stage. When the shear load exceeds elastic boundary, nonlinear energy dissipation takes place. Validations with experiments show that the proposed model provides good conformities with direct shear curves and hysteresis loops, and can predict the energy dissipation characteristics of rock joints under different working conditions. Compared to the constitutive models using Weibull's distribution, the proposed one is smooth at the elastic boundary and can accurately capture the maximum shear stress. Unlike the existing incremental-type models, the proposed one provides clear and direct analytical expressions for both shear stress and energy dissipation during the whole displacement domain, which is more convenient in application.

Nonaffine Network Structural Model for Molten Low-Density Polyethylene and High-Density Polyethylene in Oscillatory Shear

We propose molten polymer's entanglement network deformation to be nonaffine and use transient network structural theory with the revised Liu's kinetics rate equation and the revised upper convected Maxwell constitutive equation to establish a nonaffine network structural constitutive model for studying the rheological behavior of molten Low Density Polyethylene (LDPE) and High Density Polyethylene (HDPE) in oscillatory shear. As a result, when the strain amplitude or frequency increases, the shear stress amplitude increases. At the same time, the accuracy of the nonaffine network model is higher than that of affine network model. It is clear that there is a small amount of nonaffine network deformation for LDPE melts which have long chain branches, and there is a larger amount of nonaffine network deformation in oscillatory shear for HDPE melts which has no long chain branches. So we had better consider the network deformation nonaffine when we establish the constitutive equations of polymer melts in oscillatory shear.

Analytical model of shear mechanical behaviour of bolted rock joints considering influence of normal stress on bolt guide rail effect

Rock bolts have been widely used in slopes as a reinforcement measure.Modelling the shear mechanical behaviours of bolted rock joints is very complicated due to the complex factors that affect the axial force and shear force on the bolts.Rock bolts under shear action exhibit the guide rail effect;that is,the rock mass slides along the rock bolt as if the rock bolt is a rail.The normal stress can inhibit the guide rail effect and reduce the axial force on bolts.However,this factor is not considered by the existing analysis models.Shear tests of bolted joints under different normal stresses were carried out in the laboratory.During the test,the axial force on each point monitored on the bolt was recorded by a strain gauge,and the attenuation trend of the strain was studied.An analytical model that considers the inhibition of the bolt rail effect due to an increase in the normal stress was proposed to predict the shear mechanical behaviour of rock bolted joints.The new model accommodates the bolt shear behaviours in the elastic stage and plastic stage,and the estimated values agree well with the results of the direct shear tests in the laboratory.The validation shows that the proposed model can effectively describe the deformation characteristics of the bolts in the shear tests.

The Analysis of Wall Shear Stress Modulated by Acute Exercise in the Human Common Carotid Artery with an Elastic Tube Model

Assessment of the magnitude and pattern of wall shear stress(WSS)in vivo is the prerequisite for studying the quantitative relationship between exercise-induced WSS and arterial endothelial function.In the previous studies,the calculation of the WSS modulated by exercise training was primarily based upon the rigid tube model,which did not take non-linear effects of vessel elastic deformation into consideration.In this study,with an elastic tube model,we estimated the effect of a bout of 30-minute acute cycling exercise on the WSS and the flow rate in the common carotid artery according to the measured inner diameter,center-line blood flow velocity,heart rates and the brachial blood pressures before and after exercise training.Furthermore,the roles of exerciseinduced arterial diameter and blood flow rate in the change of WSS were also determined.The numerical results demonstrate that acute exercise significantly increases the magnitudes of blood flow rate and WSS.Moreover,the vessel elastic deformation is a non-negligible factor in the calculation of the WSS induced by exercise,which generates greater effects on the minimum WSS than the maximum WSS.Additionally,the contributions of exercise-induced variations in blood flow rate and diameter are almost identical in the change of the mean WSS.

Dynamic modeling and control of extracellular ATP concentration on vascular endothelial cells via shear stress modulation

A new dynamic model for cell-deformation-induced adenosine triphosphate （ATP） release from vascular endothelial cells （VECs） is proposed in this paper to quantify the relationship between the ATP concentration at the surface of VECs and blood flow-induced shear stress. The simulation results demonstrate that ATP concentration at the surface of VECs predicted by the proposed new dynamic model is more consistent with the experimental observations than those by the existing static and dynamic models. Furthermore, it is the first time that a proportional-integral-derivative （PID） feedback controller is applied to modulate extracellular ATP concentration. Three types of desired ATP concentration profiles including constant, square wave and sinusoid are obtained by regulating the wall shear stress under this PID control. The systematic methodology utilized in this paper to model and control ATP release from VECs via adjusting external stimulus opens up a new scenario where quantitative investigations into the underlying mechanisms for many biochemical phenomena can be carded out for the sake of controlling specific cellular events.