Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane...Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state. Keywords generalized non-linear strength theory (GNST) - transformed stress - constitutive model - application展开更多
The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively in its own plane is investigated and the anomalous diffusion problems of the stress field an...The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution; the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile at a given point, and the time history can be described by the fractional calculus.展开更多
Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Tim...Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Timoshenko nanobeam.The equations of motion of the nanoscale pipe are obtained based on Hamilton＇s principle and the Gurtin-Murdoch continuum elasticity incorporating the surface stress effect.Afterwards,the generalized differential quadrature method is employed to discretize the governing equations and associated boundary conditions.To what extent important parameters such as the thickness,material and surface stress modulus,residual surface stress,surface density,and boundary conditions influence the natural frequency of nanoscale pipes and the critical velocity of fluid is discussed.展开更多
The generalized lattice Boltzmann equation(GLBE),with the addition of the standard Smagorinsky subgrid-stress(SGS) model,has been proved that it is more suitable for simulating high Reynolds number turbulent flows whe...The generalized lattice Boltzmann equation(GLBE),with the addition of the standard Smagorinsky subgrid-stress(SGS) model,has been proved that it is more suitable for simulating high Reynolds number turbulent flows when compared with the lattice BGK Boltzmann equation(LBGK).However,the computing efficiency of lattice Boltzmann method(LBM) is too low to make it for practical applications,unless using a massive parallel computing clusters facility.In this study,the massive parallel computing power from an inexpensive graphic processor unit(GPU) and a typical personal computer has been developed for improving the computing efficiency,more than 100 times.This developed three-dimensional(3-D) GLBE-SGS model,with the D3Q19 scheme for simplifying collision and streaming courses,has been successfully used to study 3-D rectangular cavity flows with Reynolds number up to 10000.展开更多
Micron-scale crack propagation in red-bed soft rocks under hydraulic action is a common cause of engineering disasters due to damage to the hard rockesoft rockewater interface.Previous studies have not provided a theo...Micron-scale crack propagation in red-bed soft rocks under hydraulic action is a common cause of engineering disasters due to damage to the hard rockesoft rockewater interface.Previous studies have not provided a theoretical analysis of the length,inclination angle,and propagation angle of micron-scale cracks,nor have they established appropriate criteria to describe the crack propagation process.The propagation mechanism of micron-scale cracks in red-bed soft rocks under hydraulic action is not yet fully understood,which makes it challenging to prevent engineering disasters in these types of rocks.To address this issue,we have used the existing generalized maximum tangential stress(GMTS)and generalized maximum energy release rate(GMERR)criteria as the basis and introduced parameters related to micron-scale crack propagation and water action.The GMTS and GMERR criteria for micronscale crack propagation in red-bed soft rocks under hydraulic action(abbreviated as the Wmic-GMTS and Wmic-GMERR criteria,respectively)were established to evaluate micron-scale crack propagation in redbed soft rocks under hydraulic action.The influence of the parameters was also described.The process of micron-scale crack propagation under hydraulic action was monitored using uniaxial compression tests(UCTs)based on digital image correlation(DIC)technology.The study analyzed the length,propagation and inclination angles,and mechanical parameters of micron-scale crack propagation to confirm the reliability of the established criteria.The findings suggest that the Wmic-GMTS and Wmic-GMERR criteria are effective in describing the micron-scale crack propagation in red-bed soft rocks under hydraulic action.This study discusses the mechanism of micron-scale crack propagation and its effect on engineering disasters under hydraulic action.It covers topics such as the internal-external weakening of nano-scale particles,lateral propagation of micron-scale cracks,weakening of the mechanical properties of millimeter-scale soft rocks,and resulting int展开更多
The occurrence of geological hazards and the instability of geotechnical engineering structures are closely related to the time-dependent behavior of rock.However,the idealization boundary condition for constant stres...The occurrence of geological hazards and the instability of geotechnical engineering structures are closely related to the time-dependent behavior of rock.However,the idealization boundary condition for constant stress in creep or constant strain in relaxation is not usually attained in natural geological systems.Therefore,generalized relaxation tests that explore the simultaneous changes of stress and strain with time under different stress levels with constant pore-water pressure are conducted in this study.The results show that in area Ⅰ,area Ⅱ,and area Ⅲ,the stress and strain both change synchronously with time and show similar evolutionary laws as the strain-time curve for creep or the stress-time curve for relaxation.When the applied stress level surpasses the δ_(ci) or δ_(cd) threshold,the variations in stress and strain and their respective rates of change exhibit a significant increase.The radial deformation and its rate of change exhibit greater sensitivity in response to stress levels.The apparent strain deforms homogeneously at the primary stage,and subsequently,gradually localizes due to the microcrack development at the secondary stage.Ultimately,interconnection of the microcracks causes the formation of a shear-localization zone at the tertiary stage.The strain-time responses inside and outside the localization zone are characterized by local strain accumulation and inelastic unloading during the secondary and tertiary stages,respectively.The width of the shear-localization zone is found to range from 4.43 mm to 7.08 mm and increased with a longer time-to-failure.Scanning electron microscopy(SEM)reveals a dominant coalescence of intergranular cracks on the fracture surface,and the degree of physiochemical deterioration caused by water-rock interaction is more severe under a longer lifetime.The brittle sandstone’s time-dependent deformation is essentially controlled by microcrack development during generalized relaxation,and its expectancy-life is determined by its initial microstructural 展开更多
The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a...The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a linear formulation of phase field and computationally attractive,but stiffness reduction happens even at low strain.In this paper,generalized polynomial degradation functions are investigated to solve this problem.The first derivative of degradation function at zero phase is added as an extra constraint,which renders higher-order polynomial degradation function and nonlinear formulation of phase field.Compared with other degradation functions(like algebraic fraction function,exponential function,and trigonometric function),this polynomial degradation function enables phase in[0,1](should still avoid the first derivative of degradation function at zero phase to be 0),so there is noconvergence problem.The good and meaningful finding is that,under the same fracture strength,the proposed phase field model has a larger length scale,which means larger element size and better computational efficiency.This proposed phase field model is implemented in LS-DYNA user-defined element and user-defined material and solved by the Newton-Raphson method.A tensile test shows that the first derivative of degradation function at zero phase does impact stress-strain curve.Mode I,mode II,and mixed-mode examples show the feasibility of the proposed phase field model in simulating brittle fracture.展开更多
The asymmetric semi-circular bend(ASCB)specimen has been proposed to investigate the cracking behavior in different geo and construction materials and attracted the attention of researchers due to its advantages.Howev...The asymmetric semi-circular bend(ASCB)specimen has been proposed to investigate the cracking behavior in different geo and construction materials and attracted the attention of researchers due to its advantages.However,there are few studies on the fracture toughness determination of rock materials.In this work,a series of fracture tests were performed with the ASCB specimens made of granite.The onset of fracture,crack initiation angle and crack propagating trajectory was analyzed in detail combined with several mixed mode fracture criteria.The influence of the crack length on the mode Ⅰ/Ⅱ fracture toughness was studied.A comparison between the fracture toughness ratios predicted by varying criteria and experimental results was conducted.The relationship between experimentally determined crack initiation angles and curves of the generalized maximum tangential stress(GMTS)criterion was obtained.The fracture process of the specimen was recorded with the high-speed camera.The shortcomings of the ASCB specimens for the fracture toughness determination of rock materials were discussed.The results may provide a reference for analysis of mixed mode I and II fracture behavior of brittle materials.展开更多
In this paper,the statistical inference for system stress-strength reliability with bounded strength is discussed.When the stress and strength variables follow the three-parameter Exponentiated-Weibull distributions w...In this paper,the statistical inference for system stress-strength reliability with bounded strength is discussed.When the stress and strength variables follow the three-parameter Exponentiated-Weibull distributions with unequal scale and shape parameters,the maximum likelihood estimator(MLE)and bootstrap-p confidence interval for system reliability are derived.In addition,combining the score equations which are got by taking the first derivative of the log-likelihood function with respect to the model parameters,the modified generalized pivotal quantity for the system reliability is obtained.After that,two point estimators and a modified generalized confidence interval based on the modified generalized pivotal quantity for the system reliability are derived.Monte Carlo simulations are performed to compare the performances of the proposed point estimators and confidence intervals.Finally,a real data analysis is provided to illustrate the proposed procedures.展开更多
Based on the general solution given to a kind of linear tensor equations,the spin of a symmetric tensor is derived in an invariant form.The result is applied to find the spins of the left and the tight stretch tensors...Based on the general solution given to a kind of linear tensor equations,the spin of a symmetric tensor is derived in an invariant form.The result is applied to find the spins of the left and the tight stretch tensors and the relation among different rotation rate tensors has been discussed.According to work conjugacy,the relations between Cauchy stress and the stresses conjugate to Hill's generalized strains are obtained.Particularly,the logarithmic strain,its time rate and the conjugate stress have been discussed in de- tail.These results are important in modeling the constitutive relations for finite deformations in continuum me- chanics.展开更多
Based on the continuum physics and taking into account variation of the heat dissipation, Helmholtz free ener-gy, internal energy and exothermicity with the thermodynamic process, in this paper, the functional equatio...Based on the continuum physics and taking into account variation of the heat dissipation, Helmholtz free ener-gy, internal energy and exothermicity with the thermodynamic process, in this paper, the functional equations of the general-ized stress and entropy associated ivith the time and temperature are derived for the irreversible process of thermoviscoelastic-plastic materials. As an example, the response functionals of Maxwell viscoelastic materials are obtained.展开更多
In order to estimate the reliability of wind turbine gearbox based on the system level, a generalized stress-strength model is introduced. Considering that the system works properly under a variety of random stresses ...In order to estimate the reliability of wind turbine gearbox based on the system level, a generalized stress-strength model is introduced. Considering that the system works properly under a variety of random stresses which affect every component, the total stress on the system is given by a known linear combination of the stresses of all components. Then the strength of the system can be viewed as a linear combination of the strengths of relative components. In this model, stress and strength are independent of each other. Reliability of the system is the probability that strength exceeds stress. Finally, the reliability of wind turbine gearbox is estimated by the multivariable reliability calculation method. The corresponding result is compared with the results of reliability in the extreme cases(completely dependent and completely independent) by the traditional evaluation method.展开更多
基金the National Natural Science Foundation of China ( Grant No. 10272010) the Ministry of Science and Technology of China (Grant No. 2002CCC00200).
文摘Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state. Keywords generalized non-linear strength theory (GNST) - transformed stress - constitutive model - application
基金the Doctoral Program Foundation of the Education Ministry of China the National Natural Science Foundation of China (Grant No. 10002003) Foundation for University Key Teacher by the Ministry of Education of China.
文摘The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution; the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile at a given point, and the time history can be described by the fractional calculus.
文摘Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Timoshenko nanobeam.The equations of motion of the nanoscale pipe are obtained based on Hamilton＇s principle and the Gurtin-Murdoch continuum elasticity incorporating the surface stress effect.Afterwards,the generalized differential quadrature method is employed to discretize the governing equations and associated boundary conditions.To what extent important parameters such as the thickness,material and surface stress modulus,residual surface stress,surface density,and boundary conditions influence the natural frequency of nanoscale pipes and the critical velocity of fluid is discussed.
基金supported by the Virginia Institute of Marine Science,College of William and Mary for the Study Environmentthe National Natural Science Foundation of China(Grant No.50679008)
文摘The generalized lattice Boltzmann equation(GLBE),with the addition of the standard Smagorinsky subgrid-stress(SGS) model,has been proved that it is more suitable for simulating high Reynolds number turbulent flows when compared with the lattice BGK Boltzmann equation(LBGK).However,the computing efficiency of lattice Boltzmann method(LBM) is too low to make it for practical applications,unless using a massive parallel computing clusters facility.In this study,the massive parallel computing power from an inexpensive graphic processor unit(GPU) and a typical personal computer has been developed for improving the computing efficiency,more than 100 times.This developed three-dimensional(3-D) GLBE-SGS model,with the D3Q19 scheme for simplifying collision and streaming courses,has been successfully used to study 3-D rectangular cavity flows with Reynolds number up to 10000.
基金funded by the National Natural Science Foundation of China(NSFC)(Grant Nos.42293354,42293351,and 42277131).
文摘Micron-scale crack propagation in red-bed soft rocks under hydraulic action is a common cause of engineering disasters due to damage to the hard rockesoft rockewater interface.Previous studies have not provided a theoretical analysis of the length,inclination angle,and propagation angle of micron-scale cracks,nor have they established appropriate criteria to describe the crack propagation process.The propagation mechanism of micron-scale cracks in red-bed soft rocks under hydraulic action is not yet fully understood,which makes it challenging to prevent engineering disasters in these types of rocks.To address this issue,we have used the existing generalized maximum tangential stress(GMTS)and generalized maximum energy release rate(GMERR)criteria as the basis and introduced parameters related to micron-scale crack propagation and water action.The GMTS and GMERR criteria for micronscale crack propagation in red-bed soft rocks under hydraulic action(abbreviated as the Wmic-GMTS and Wmic-GMERR criteria,respectively)were established to evaluate micron-scale crack propagation in redbed soft rocks under hydraulic action.The influence of the parameters was also described.The process of micron-scale crack propagation under hydraulic action was monitored using uniaxial compression tests(UCTs)based on digital image correlation(DIC)technology.The study analyzed the length,propagation and inclination angles,and mechanical parameters of micron-scale crack propagation to confirm the reliability of the established criteria.The findings suggest that the Wmic-GMTS and Wmic-GMERR criteria are effective in describing the micron-scale crack propagation in red-bed soft rocks under hydraulic action.This study discusses the mechanism of micron-scale crack propagation and its effect on engineering disasters under hydraulic action.It covers topics such as the internal-external weakening of nano-scale particles,lateral propagation of micron-scale cracks,weakening of the mechanical properties of millimeter-scale soft rocks,and resulting int
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52304099,52172625)Shenzhen Science and Technology Program(Grant No.RCYX20221008092903013).
文摘The occurrence of geological hazards and the instability of geotechnical engineering structures are closely related to the time-dependent behavior of rock.However,the idealization boundary condition for constant stress in creep or constant strain in relaxation is not usually attained in natural geological systems.Therefore,generalized relaxation tests that explore the simultaneous changes of stress and strain with time under different stress levels with constant pore-water pressure are conducted in this study.The results show that in area Ⅰ,area Ⅱ,and area Ⅲ,the stress and strain both change synchronously with time and show similar evolutionary laws as the strain-time curve for creep or the stress-time curve for relaxation.When the applied stress level surpasses the δ_(ci) or δ_(cd) threshold,the variations in stress and strain and their respective rates of change exhibit a significant increase.The radial deformation and its rate of change exhibit greater sensitivity in response to stress levels.The apparent strain deforms homogeneously at the primary stage,and subsequently,gradually localizes due to the microcrack development at the secondary stage.Ultimately,interconnection of the microcracks causes the formation of a shear-localization zone at the tertiary stage.The strain-time responses inside and outside the localization zone are characterized by local strain accumulation and inelastic unloading during the secondary and tertiary stages,respectively.The width of the shear-localization zone is found to range from 4.43 mm to 7.08 mm and increased with a longer time-to-failure.Scanning electron microscopy(SEM)reveals a dominant coalescence of intergranular cracks on the fracture surface,and the degree of physiochemical deterioration caused by water-rock interaction is more severe under a longer lifetime.The brittle sandstone’s time-dependent deformation is essentially controlled by microcrack development during generalized relaxation,and its expectancy-life is determined by its initial microstructural
文摘The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a linear formulation of phase field and computationally attractive,but stiffness reduction happens even at low strain.In this paper,generalized polynomial degradation functions are investigated to solve this problem.The first derivative of degradation function at zero phase is added as an extra constraint,which renders higher-order polynomial degradation function and nonlinear formulation of phase field.Compared with other degradation functions(like algebraic fraction function,exponential function,and trigonometric function),this polynomial degradation function enables phase in[0,1](should still avoid the first derivative of degradation function at zero phase to be 0),so there is noconvergence problem.The good and meaningful finding is that,under the same fracture strength,the proposed phase field model has a larger length scale,which means larger element size and better computational efficiency.This proposed phase field model is implemented in LS-DYNA user-defined element and user-defined material and solved by the Newton-Raphson method.A tensile test shows that the first derivative of degradation function at zero phase does impact stress-strain curve.Mode I,mode II,and mixed-mode examples show the feasibility of the proposed phase field model in simulating brittle fracture.
基金Projects(52004182,51804110,51904101)supported by the National Natural Science Foundation of ChinaProject(2020JJ5188)supported by the Natural Science Foundation of Hunan Province,China。
文摘The asymmetric semi-circular bend(ASCB)specimen has been proposed to investigate the cracking behavior in different geo and construction materials and attracted the attention of researchers due to its advantages.However,there are few studies on the fracture toughness determination of rock materials.In this work,a series of fracture tests were performed with the ASCB specimens made of granite.The onset of fracture,crack initiation angle and crack propagating trajectory was analyzed in detail combined with several mixed mode fracture criteria.The influence of the crack length on the mode Ⅰ/Ⅱ fracture toughness was studied.A comparison between the fracture toughness ratios predicted by varying criteria and experimental results was conducted.The relationship between experimentally determined crack initiation angles and curves of the generalized maximum tangential stress(GMTS)criterion was obtained.The fracture process of the specimen was recorded with the high-speed camera.The shortcomings of the ASCB specimens for the fracture toughness determination of rock materials were discussed.The results may provide a reference for analysis of mixed mode I and II fracture behavior of brittle materials.
基金supported by the National Natural Science Foundation of China under Grant Nos.12101475,12101476,11901134,12061091the Soft Science Project of Xi’an under Grant No.22RKYJ0065+1 种基金the Natural Science Basic Research Program of Shaanxi under Grant Nos.2021JQ-186,2020JQ-285the Fundamental Research Funds for the Central Universities under Grant Nos.XJS210603,JGYB2222。
文摘In this paper,the statistical inference for system stress-strength reliability with bounded strength is discussed.When the stress and strength variables follow the three-parameter Exponentiated-Weibull distributions with unequal scale and shape parameters,the maximum likelihood estimator(MLE)and bootstrap-p confidence interval for system reliability are derived.In addition,combining the score equations which are got by taking the first derivative of the log-likelihood function with respect to the model parameters,the modified generalized pivotal quantity for the system reliability is obtained.After that,two point estimators and a modified generalized confidence interval based on the modified generalized pivotal quantity for the system reliability are derived.Monte Carlo simulations are performed to compare the performances of the proposed point estimators and confidence intervals.Finally,a real data analysis is provided to illustrate the proposed procedures.
基金The project is supported by the National Natural Science Foundation of Chinathe Chinese Academy of Sciences(No.87-52)
文摘Based on the general solution given to a kind of linear tensor equations,the spin of a symmetric tensor is derived in an invariant form.The result is applied to find the spins of the left and the tight stretch tensors and the relation among different rotation rate tensors has been discussed.According to work conjugacy,the relations between Cauchy stress and the stresses conjugate to Hill's generalized strains are obtained.Particularly,the logarithmic strain,its time rate and the conjugate stress have been discussed in de- tail.These results are important in modeling the constitutive relations for finite deformations in continuum me- chanics.
文摘Based on the continuum physics and taking into account variation of the heat dissipation, Helmholtz free ener-gy, internal energy and exothermicity with the thermodynamic process, in this paper, the functional equations of the general-ized stress and entropy associated ivith the time and temperature are derived for the irreversible process of thermoviscoelastic-plastic materials. As an example, the response functionals of Maxwell viscoelastic materials are obtained.
基金the National Natural Science Foundation of China(No.51265025)
文摘In order to estimate the reliability of wind turbine gearbox based on the system level, a generalized stress-strength model is introduced. Considering that the system works properly under a variety of random stresses which affect every component, the total stress on the system is given by a known linear combination of the stresses of all components. Then the strength of the system can be viewed as a linear combination of the strengths of relative components. In this model, stress and strength are independent of each other. Reliability of the system is the probability that strength exceeds stress. Finally, the reliability of wind turbine gearbox is estimated by the multivariable reliability calculation method. The corresponding result is compared with the results of reliability in the extreme cases(completely dependent and completely independent) by the traditional evaluation method.
