At present, associated flow rule of traditional plastic theory is adopted in the slip line field theory and upper bound method of geotechnical materials. So the stress characteristic line conforms to the velocity line...At present, associated flow rule of traditional plastic theory is adopted in the slip line field theory and upper bound method of geotechnical materials. So the stress characteristic line conforms to the velocity line. It is proved that geotechnical materials do not abide by the associated flow rule. It is impossible for the stress characteristic line to conform to the velocity line. Generalized plastic mechanics theoretically proved that plastic potential surface intersects the Mohr-Coulomb yield surface with an angle, so that the velocity line must be studied by non-associated flow rule. According to limit analysis theory, the theory of slip line field is put forward in this paper, and then the ultimate beating capacity of strip footing is obtained based on the associated flow rule and the non-associated flow nile individually. These two results are identical since the ultimate bearing capacity is independent of flow role. On the contrary, the velocity fields of associated and non-associated flow rules are different which shows the velocity field based on the associat- ed flow rule is incorrect.展开更多
The required reinforcement force to prevent instability and the yield acceleration of reinforced slopes are computed under seismic loading by applying the kinematic approach of limit analysis in conjunction with the p...The required reinforcement force to prevent instability and the yield acceleration of reinforced slopes are computed under seismic loading by applying the kinematic approach of limit analysis in conjunction with the pseudo-dynamic method for a wide range of soil cohesion, friction angle, dilation angle and horizontal and vertical seismic coefficients. Each parameter threatening the stability of the slope enhances the magnitude of the required reinforcement force and vice versa. Moreover, the yield acceleration increases with the increase in soil shear strength parameters but decreases with the increase in the slope angle. The comparison of the present work with some of the available solutions in the literatures shows a reasonable agreement.展开更多
The geological hazards, such as water inrush and mud outburst, are easily induced by the high water pressure caverns ahead of a karst tunnel face. Therefore, it is a pivotal issue to determine the reserved thickness o...The geological hazards, such as water inrush and mud outburst, are easily induced by the high water pressure caverns ahead of a karst tunnel face. Therefore, it is a pivotal issue to determine the reserved thickness of rock plug during the construction of tunnels. The limit analysis principle is employed to analyze the safe thickness from the point of energy dissipation, and the nonlinear and non-associated characteristics of geotechnical materials are both considered. On the basis of a plane failure pattern of rock plug, the expressions of detaching curve and rock plug thickness are derived. The effect of each parameter on the safe thickness of rock plug is discussed in detail, which interprets the corresponding failure scope of rock plug. The obtained results indicate that the thickness of rock plug is highly influenced by the nonlinear dilatancy coefficient and the nonlinear coefficient. The proposed method is validated by a comparison of the calculated results with those of the engineering project of the "526 karst cavern" of Yunwushan tunnel. This proposed method can provide reference basis for the design and excavation of karst tunnels in the future.展开更多
Seismic failure mechanisms were investigated for soil slopes subjected to strip load with upper bound method of limit analysis and finite difference method of numerical simulation,considering the influence of associat...Seismic failure mechanisms were investigated for soil slopes subjected to strip load with upper bound method of limit analysis and finite difference method of numerical simulation,considering the influence of associated and nonassociated flow rules.Quasi-static representation of soil inertia effects using a seismic coefficient concept was adopted for seismic failure analysis.Numerical study was conducted to investigate the influences of dilative angle and earthquake on the seismic failure mechanisms for the loaded slope,and the failure mechanisms for different dilation angles were compared.The results show that dilation angle has influences on the seismic failure surfaces,that seismic maximum displacement vector decreases as the dilation angle increases,and that seismic maximum shear strain rate decreases as the dilation angle increases.展开更多
Seismic bearing capacity factors of a strip footing placed on soil slope were determined with both associated and nonassociated flow rules. Quasi-static representation of earthquake effects using a seismic coefficient...Seismic bearing capacity factors of a strip footing placed on soil slope were determined with both associated and nonassociated flow rules. Quasi-static representation of earthquake effects using a seismic coefficient concept was adopted for seismic bearing capacity calculations. A multi-wedge translational failure mechanism was used to obtain the seismic bearing capacity factors for different seismic coefficients and various inclined angles. Employing the associated flow rule, numerical results were compared with the published solutions. For bearing capacity factors related to cohesion and equivalent surcharge load, the maximum difference approximates 0.1%. However, the difference of bearing capacity factor related to unit weight is larger. With the two flow rules, the seismic bearing capacity factors were presented in the form of design charts for practical use. The results show that seismic bearing capacity factors related to the cohesion, the equivalent surcharge load and the unit weight increase greatly as the dilatancy angle increases, and that the nonassociated flow rule has important influences on the seismic bearing capacity.展开更多
The influences of soil dilatancy angle on three-dimensional （3D） seismic stability of locally-loaded slopes in nonassociated flow rule materials were investigated using a new rotational collapse mechanism and quasi-...The influences of soil dilatancy angle on three-dimensional （3D） seismic stability of locally-loaded slopes in nonassociated flow rule materials were investigated using a new rotational collapse mechanism and quasi-static coefficient concept. Extended Bishop method and Boussinesq theorem were employed to establish the stress distribution along the rupture surfaces that are required to obtain the rate of internal energy dissipation for the nonassociated flow rule materials in rotational collapse mechanisms. Good agreement was observed by comparing the current results with those obtained using the translational or rotational mechanisms and numerical finite difference method. The results indicate that the seismic stability of slopes reduces by decreasing the dilatancy angle for nonassociated flow rule materials. The amount of the mentioned decrease is more significant in the case of mild slopes in frictional soils. A nearly infinite slope under local loading, whether its critical failure surface is 2D or 3D, not only depends on the magnitude of the external load, but also depends on the dilataney angle of soil and the coefficient of seismic load.展开更多
On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent me...On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure,surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.展开更多
The Burzynski criterion is developed for anisotropic asymmetric metals with the non-associated flow rule （NAFR） for plane stress problems. The presented pressure depending on the yield criterion can be calibrated wi...The Burzynski criterion is developed for anisotropic asymmetric metals with the non-associated flow rule （NAFR） for plane stress problems. The presented pressure depending on the yield criterion can be calibrated with ten experimental data, i.e., the tensile yield stresses at 0°, 45°, and 90°, the compressive yield stresses at 0°, 15°, 30°, 45°, 75°, and 90° from the rolling direction, and the biaxial tensile yield stress. The corresponding pressure independent plastic potential function can be calibrated with six experimental data, i.e., the tensile R-values at 0°, 15°, 45°, 75°, and 90° from the rolling direction and the tensile biaxial R-value. The downhill simplex method is used to solve these ten and six high nonlinear equations for the yield and plastic potential functions, respectively. The results show that the presented new criterion is appropriate for anisotropic asymmetric metals.展开更多
A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional ...A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional flow rule.The yield function includes parameters that govern the evolution of yield surface,enabling an accurate description of three-dimensional stress states.The direction of plastic flow is governed by the two different fractional orders,which are functions of the plastic internal variable.Additionally,a detailed process is proposed for identifying the yield function parameters and fractional orders.Subsequently,the relationship between the fractional order and the direction of plastic flow in the meridian and deviatoric planes is examined,characterized by the dilation angle and the plastic deflection angle,respectively.The non-orthogonal flow rule,also referred to as the fractional flow rule,allows for a border range of plastic deflection and dilation angles compared to the orthogonal flow rule,thereby significantly enhancing its applicability.The validity and accuracy of proposed model are verified by comparing the analytical solution of the constitutive model with the experimental data.A comparison between the non-orthogonal flow rule and orthogonal flow rule is conducted in both the deviatoric and meridian planes.The further comparison of the stress-strain curves for the non-orthogonal and orthogonal flow rules demonstrates the superiority of the fractional constitutive model.展开更多
The automotive industry increasingly relies on numerical simulations to predict the geometry and forming processes of complex curved parts.Accurate yield stress functions that cover a wide range of stress states,such ...The automotive industry increasingly relies on numerical simulations to predict the geometry and forming processes of complex curved parts.Accurate yield stress functions that cover a wide range of stress states,such as uniaxial tension,equi-biaxial tension,near-plane strain tension,and simple shear,are essential for implementing virtual manufacturing technologies.In this work,a new additive-coupled analytical yield stress function,CPN2025,is proposed to accurately describe plastic anisotropy under various loading conditions.CPN2025 integrates the Poly4 anisotropic yield criterion with the Hosford isotropic yield criterion under a non-associated flow rule.A non-fixed-exponent calibration strategy is introduced,overcoming the limitations of existing yield criteria that typically offer curvature adjustment with only positive or negative correlations.CPN2025 is compared with other non-associated yield functions,including SY2009,CQN2017,and NAFR-Poly4,to evaluate its performance in predicting the plastic anisotropy of DP490,QP1180,AA5754-O,and AA6016-T4.Results show that,while meeting convexity requirements,the additive-coupled approach not only provides greater flexibility than the multiplicative-coupled but also simplifies the acquisition of partial derivative information.CPN2025 delivers the highest accuracy in characterizing anisotropic yield behavior,particularly for near-plane strain tension and simple shear loadings.Additionally,incorporating more uniaxial tensile yield stress-calibrated material parameters significantly improves the prediction capacity of in-plane anisotropic behavior.The use of anisotropic hardening concepts enhances the model's capability to capture the subsequent yield behavior across the entire plastic strain range.展开更多
6016-T4 aluminum alloy and DP490 steel were systematically tested under 24 proportional loading paths,including uniaxial tensile tests with a 15°increment,uniaxial compressive and simple shear tests with a 45...6016-T4 aluminum alloy and DP490 steel were systematically tested under 24 proportional loading paths,including uniaxial tensile tests with a 15°increment,uniaxial compressive and simple shear tests with a 45°increment,and biaxial tensile tests using cruciform specimens.Cruciform specimens in the rolling/transverse and 45°/135°sampling directions were tested with seven and four different stress ra-tios,respectively.The normal and diagonal planes plastic work contours and the yield stresses under uniaxial tension and compression were measured to investigate the anisotropic yield.Meanwhile,the normal and diagonal planes directions of plastic strain rate and the rα-values under uniaxial tension and compression were characterized to confirm the plastic flow.Several existing asymmetric yield crite-ria under the associated and non-associated flow rules were comprehensively evaluated to describe the asymmetric plastic anisotropy of 6016-T4 aluminum alloy and DP490 steel.The results suggest that in the investigated yield criteria,the non-associated models can predict the tension and compression asym-metry of materials more accurately than the associated models,and the function of stress triaxiality can more effectively describe the asymmetric yield behavior than the first stress invariant.In addition,the pure shear stress states are helpful in assessing the validity and applicability of advanced asymmetric yield stress functions,and the inspection of diagonal plane plastic work contours containing more pure shear stress states should prioritized over that of normal plane plastic work contours.The evaluation of plastic potential functions should not only consider the prediction accuracy of the normal plane di-rections of plastic strain rate,but also further check the diagonal plane directions of plastic strain rate.Expressing mechanical properties as a function of equivalent plastic strain to calibrate parameters of the yield criterion allows the continuous capture of anisotropic evolution of the asymmetric yield surface and the changes in the asymmetric plastic potential surface.展开更多
文摘At present, associated flow rule of traditional plastic theory is adopted in the slip line field theory and upper bound method of geotechnical materials. So the stress characteristic line conforms to the velocity line. It is proved that geotechnical materials do not abide by the associated flow rule. It is impossible for the stress characteristic line to conform to the velocity line. Generalized plastic mechanics theoretically proved that plastic potential surface intersects the Mohr-Coulomb yield surface with an angle, so that the velocity line must be studied by non-associated flow rule. According to limit analysis theory, the theory of slip line field is put forward in this paper, and then the ultimate beating capacity of strip footing is obtained based on the associated flow rule and the non-associated flow nile individually. These two results are identical since the ultimate bearing capacity is independent of flow role. On the contrary, the velocity fields of associated and non-associated flow rules are different which shows the velocity field based on the associat- ed flow rule is incorrect.
文摘The required reinforcement force to prevent instability and the yield acceleration of reinforced slopes are computed under seismic loading by applying the kinematic approach of limit analysis in conjunction with the pseudo-dynamic method for a wide range of soil cohesion, friction angle, dilation angle and horizontal and vertical seismic coefficients. Each parameter threatening the stability of the slope enhances the magnitude of the required reinforcement force and vice versa. Moreover, the yield acceleration increases with the increase in soil shear strength parameters but decreases with the increase in the slope angle. The comparison of the present work with some of the available solutions in the literatures shows a reasonable agreement.
基金Project(2013CB036004) supported by the National Basic Research Program of ChinaProjects(51378510,51308072) supported by National Natural Science Foundation of ChinaProject(CX2014B069) supported by the Hunan Provincial Innovation Foundation for Postgraduate,China
文摘The geological hazards, such as water inrush and mud outburst, are easily induced by the high water pressure caverns ahead of a karst tunnel face. Therefore, it is a pivotal issue to determine the reserved thickness of rock plug during the construction of tunnels. The limit analysis principle is employed to analyze the safe thickness from the point of energy dissipation, and the nonlinear and non-associated characteristics of geotechnical materials are both considered. On the basis of a plane failure pattern of rock plug, the expressions of detaching curve and rock plug thickness are derived. The effect of each parameter on the safe thickness of rock plug is discussed in detail, which interprets the corresponding failure scope of rock plug. The obtained results indicate that the thickness of rock plug is highly influenced by the nonlinear dilatancy coefficient and the nonlinear coefficient. The proposed method is validated by a comparison of the calculated results with those of the engineering project of the "526 karst cavern" of Yunwushan tunnel. This proposed method can provide reference basis for the design and excavation of karst tunnels in the future.
基金Project(200550) supported by the Foundation for the Author of National Excellent Doctoral Dissertation of ChinaProject(200631878557) supported by the West Traffic of Science and Technology,China
文摘Seismic failure mechanisms were investigated for soil slopes subjected to strip load with upper bound method of limit analysis and finite difference method of numerical simulation,considering the influence of associated and nonassociated flow rules.Quasi-static representation of soil inertia effects using a seismic coefficient concept was adopted for seismic failure analysis.Numerical study was conducted to investigate the influences of dilative angle and earthquake on the seismic failure mechanisms for the loaded slope,and the failure mechanisms for different dilation angles were compared.The results show that dilation angle has influences on the seismic failure surfaces,that seismic maximum displacement vector decreases as the dilation angle increases,and that seismic maximum shear strain rate decreases as the dilation angle increases.
基金Project(200550) supported by the Foundation for the Author of National Excellent Doctoral Dissertation of ChinaProject(05-0686) supported by the Program for New Century Excellent Talents in University
文摘Seismic bearing capacity factors of a strip footing placed on soil slope were determined with both associated and nonassociated flow rules. Quasi-static representation of earthquake effects using a seismic coefficient concept was adopted for seismic bearing capacity calculations. A multi-wedge translational failure mechanism was used to obtain the seismic bearing capacity factors for different seismic coefficients and various inclined angles. Employing the associated flow rule, numerical results were compared with the published solutions. For bearing capacity factors related to cohesion and equivalent surcharge load, the maximum difference approximates 0.1%. However, the difference of bearing capacity factor related to unit weight is larger. With the two flow rules, the seismic bearing capacity factors were presented in the form of design charts for practical use. The results show that seismic bearing capacity factors related to the cohesion, the equivalent surcharge load and the unit weight increase greatly as the dilatancy angle increases, and that the nonassociated flow rule has important influences on the seismic bearing capacity.
文摘The influences of soil dilatancy angle on three-dimensional （3D） seismic stability of locally-loaded slopes in nonassociated flow rule materials were investigated using a new rotational collapse mechanism and quasi-static coefficient concept. Extended Bishop method and Boussinesq theorem were employed to establish the stress distribution along the rupture surfaces that are required to obtain the rate of internal energy dissipation for the nonassociated flow rule materials in rotational collapse mechanisms. Good agreement was observed by comparing the current results with those obtained using the translational or rotational mechanisms and numerical finite difference method. The results indicate that the seismic stability of slopes reduces by decreasing the dilatancy angle for nonassociated flow rule materials. The amount of the mentioned decrease is more significant in the case of mild slopes in frictional soils. A nearly infinite slope under local loading, whether its critical failure surface is 2D or 3D, not only depends on the magnitude of the external load, but also depends on the dilataney angle of soil and the coefficient of seismic load.
基金Project(2013CB036004) supported by the National Basic Research Program of ChinaProjects(51178468,51378510) supported by the National Natural Science Foundation of ChinaProject(CX2013B077) supported by Hunan Provincial Innovation Foundation for Postgraduate,China
文摘On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure,surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.
文摘The Burzynski criterion is developed for anisotropic asymmetric metals with the non-associated flow rule （NAFR） for plane stress problems. The presented pressure depending on the yield criterion can be calibrated with ten experimental data, i.e., the tensile yield stresses at 0°, 45°, and 90°, the compressive yield stresses at 0°, 15°, 30°, 45°, 75°, and 90° from the rolling direction, and the biaxial tensile yield stress. The corresponding pressure independent plastic potential function can be calibrated with six experimental data, i.e., the tensile R-values at 0°, 15°, 45°, 75°, and 90° from the rolling direction and the tensile biaxial R-value. The downhill simplex method is used to solve these ten and six high nonlinear equations for the yield and plastic potential functions, respectively. The results show that the presented new criterion is appropriate for anisotropic asymmetric metals.
基金sponsored by the National Natural Science Foundation of China(Grant No.42141010).
文摘A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional flow rule.The yield function includes parameters that govern the evolution of yield surface,enabling an accurate description of three-dimensional stress states.The direction of plastic flow is governed by the two different fractional orders,which are functions of the plastic internal variable.Additionally,a detailed process is proposed for identifying the yield function parameters and fractional orders.Subsequently,the relationship between the fractional order and the direction of plastic flow in the meridian and deviatoric planes is examined,characterized by the dilation angle and the plastic deflection angle,respectively.The non-orthogonal flow rule,also referred to as the fractional flow rule,allows for a border range of plastic deflection and dilation angles compared to the orthogonal flow rule,thereby significantly enhancing its applicability.The validity and accuracy of proposed model are verified by comparing the analytical solution of the constitutive model with the experimental data.A comparison between the non-orthogonal flow rule and orthogonal flow rule is conducted in both the deviatoric and meridian planes.The further comparison of the stress-strain curves for the non-orthogonal and orthogonal flow rules demonstrates the superiority of the fractional constitutive model.
基金financial support from the National Natural Science Foundation of China(Grant Nos.52305396,52371116,and 52375310)support of the research fellowship from the Alexander von Humboldt Foundation.
文摘The automotive industry increasingly relies on numerical simulations to predict the geometry and forming processes of complex curved parts.Accurate yield stress functions that cover a wide range of stress states,such as uniaxial tension,equi-biaxial tension,near-plane strain tension,and simple shear,are essential for implementing virtual manufacturing technologies.In this work,a new additive-coupled analytical yield stress function,CPN2025,is proposed to accurately describe plastic anisotropy under various loading conditions.CPN2025 integrates the Poly4 anisotropic yield criterion with the Hosford isotropic yield criterion under a non-associated flow rule.A non-fixed-exponent calibration strategy is introduced,overcoming the limitations of existing yield criteria that typically offer curvature adjustment with only positive or negative correlations.CPN2025 is compared with other non-associated yield functions,including SY2009,CQN2017,and NAFR-Poly4,to evaluate its performance in predicting the plastic anisotropy of DP490,QP1180,AA5754-O,and AA6016-T4.Results show that,while meeting convexity requirements,the additive-coupled approach not only provides greater flexibility than the multiplicative-coupled but also simplifies the acquisition of partial derivative information.CPN2025 delivers the highest accuracy in characterizing anisotropic yield behavior,particularly for near-plane strain tension and simple shear loadings.Additionally,incorporating more uniaxial tensile yield stress-calibrated material parameters significantly improves the prediction capacity of in-plane anisotropic behavior.The use of anisotropic hardening concepts enhances the model's capability to capture the subsequent yield behavior across the entire plastic strain range.
基金the Promotion China Ph.D.Pro-gram of BMW Brilliance Automotive Ltd.and Beijing Municipal Ed-ucation Commission and Beijing Municipal Natural Science Foun-dation(No.KZ200010009041)for financial support and KOBELCO and TAGAL for providing commercial automotive sheets.
文摘6016-T4 aluminum alloy and DP490 steel were systematically tested under 24 proportional loading paths,including uniaxial tensile tests with a 15°increment,uniaxial compressive and simple shear tests with a 45°increment,and biaxial tensile tests using cruciform specimens.Cruciform specimens in the rolling/transverse and 45°/135°sampling directions were tested with seven and four different stress ra-tios,respectively.The normal and diagonal planes plastic work contours and the yield stresses under uniaxial tension and compression were measured to investigate the anisotropic yield.Meanwhile,the normal and diagonal planes directions of plastic strain rate and the rα-values under uniaxial tension and compression were characterized to confirm the plastic flow.Several existing asymmetric yield crite-ria under the associated and non-associated flow rules were comprehensively evaluated to describe the asymmetric plastic anisotropy of 6016-T4 aluminum alloy and DP490 steel.The results suggest that in the investigated yield criteria,the non-associated models can predict the tension and compression asym-metry of materials more accurately than the associated models,and the function of stress triaxiality can more effectively describe the asymmetric yield behavior than the first stress invariant.In addition,the pure shear stress states are helpful in assessing the validity and applicability of advanced asymmetric yield stress functions,and the inspection of diagonal plane plastic work contours containing more pure shear stress states should prioritized over that of normal plane plastic work contours.The evaluation of plastic potential functions should not only consider the prediction accuracy of the normal plane di-rections of plastic strain rate,but also further check the diagonal plane directions of plastic strain rate.Expressing mechanical properties as a function of equivalent plastic strain to calibrate parameters of the yield criterion allows the continuous capture of anisotropic evolution of the asymmetric yield surface and the changes in the asymmetric plastic potential surface.
