In this paper,the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading.Firstly,a coupled damage variable was derived,which contains two parts,i.e.,the compa...In this paper,the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading.Firstly,a coupled damage variable was derived,which contains two parts,i.e.,the compaction-induced damage and the cracking-induced damage.The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage,and the cracking-induced damage variable was established based on the statistical damage theory.Secondly,based on the total damage variable,a damage constitutive equation was proposed to describe the constitutive relation of rock under the monotonic uniaxial compression conditions,whereafter,the application of this model is extended to cyclic loading and unloading conditions.To validate the proposed monotonic and cyclic constitutive equations,a series of mechanical tests for marble specimens were carried out,which contained the monotonic uniaxial compression(MUC)experiment,cyclic uniaxial compression experiments under the variable amplitude(CUC-VA)and constant amplitude(CUC-CA)conditions.The results show that the proposed total damage variable comprehensively reflects the damage evolution characteristic,i.e.,the damage variable firstly decreases,then increases no matter under the conditions of MUC,CUC-VA or CUC-CA.Then a reasonable consistency is observed between the experimental and theoretical curves.The proposed cyclic constitutive equations can simulate the whole cyclic loading and unloading behaviors,such as the initial compaction,the strain hardening and the strain softening.Furthermore,the shapes of the theoretical curves are controlled by the modified coefficient,compaction sensitivity coefficient and two Weibull distributed parameters.展开更多
Thermo-Hydro-Mechanical （THM） coupling pro- cesses in unsaturated soils are very important in both theoretical researches and engineering applications. A coupled formulation based on hybrid mixture theory is derived...Thermo-Hydro-Mechanical （THM） coupling pro- cesses in unsaturated soils are very important in both theoretical researches and engineering applications. A coupled formulation based on hybrid mixture theory is derived to model the THM coupling behavior of unsaturated soils. The free-energy and dissipative functions for different phases are derived from Taylor＇s series expansions. Constitutive relations for THM coupled behaviors of unsaturated soils, which include deformation, entropy change, fluid flow, heat conduction, and dynamic compatibility conditions on the interfaces, are then established. The number of field equations is shown to be equal to the number of unknown variables; thus, a closure of this coupling problem is established. In addition to modifications of the physical conservation equations with coupling effect terms, the constitutive equations, which consider the coupling between elastoplastic deformation of the soil skeleton, fluid flow, and heat transfer, are also derived.展开更多
A constitutive equation was proposed to describe the effect of grain size on the deformation behavior.And a coupling simulation of deformation with heat transfer and microstructure was carried out in isothermal upsett...A constitutive equation was proposed to describe the effect of grain size on the deformation behavior.And a coupling simulation of deformation with heat transfer and microstructure was carried out in isothermal upsetting process of Ti60 alloy.The effects of processing parameters on the equivalent strain,the equivalent stress,the temperature rise and the grain size distribution in isothermal upsetting process of Ti60 alloy were analyzed.It is concluded that the uniformity of equivalent strain and equivalent stress increases with the increase of deformation temperature.However,the temperature rise and the grain size decreases with the increase of deformation temperature.The non-uniformity of equivalent strain,equivalent stress,temperature field and grain size increases with the increase of height reduction.And the calculated grain size using simulation is in good agreement with the experimental one.展开更多
Elasto-plastic consolidation is one of the classic coupling questions in geomechanics. To solve this problem, an elasto-plastic constitutive model is derived based on the numerical modeling method. The model is applie...Elasto-plastic consolidation is one of the classic coupling questions in geomechanics. To solve this problem, an elasto-plastic constitutive model is derived based on the numerical modeling method. The model is applied to Blot＇s consolidation theory. Incremental governing partial differential equations are established using this method. According to the stress path, the decoupling condition of these equations is discussed. Based on these conditions, an incremental diffusion equation and uncoupling governing equations are presented. The method is then applied to numerical analyses of three examples. The results show that （1） the effect of the stress path should be taken into account in the simulation of the soil consolidation question; （2） this decoupling method can predict the evolvement of pore water pressure; （3） the settlement using cam-clay model is less than that using numerical model because of dilatancy.展开更多
According to the prominent characteristic of rapid heating and cooling velocity in process of laser phase transformation hardening, it is important and necessary to consider the couple relation among temperature, phas...According to the prominent characteristic of rapid heating and cooling velocity in process of laser phase transformation hardening, it is important and necessary to consider the couple relation among temperature, phase transformation and stress. Based on the above, a mathematical model to analyze transformation and to reflect its characteristic is presented. Also temperature field control equation relative to stress and phase transformation is set up and thermal elastoplastic constitutive equation containing phase transformation was derived, In a given yield condition, temperature and stress field are numerically calculated by means of Finite Element Method. The result indicates the calculation value coincides with result of test Stress especially thermal stress varied violently in process of laser phase transformation hardening, which leaded to the residual stress on the surface and accorded to the fact. This process can improve the characteristic of material, so it is significant to study on thermal stress of laser quenching, to discuss the effect of phase transformation and stress on temperature, to optimize the laser quenching process and to improve the synthetic mechanic properties of quenching material.展开更多
基金This study was financially supported by the National Natural Science Foundation of China(Nos.51978292,42077254 and 51874144).
文摘In this paper,the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading.Firstly,a coupled damage variable was derived,which contains two parts,i.e.,the compaction-induced damage and the cracking-induced damage.The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage,and the cracking-induced damage variable was established based on the statistical damage theory.Secondly,based on the total damage variable,a damage constitutive equation was proposed to describe the constitutive relation of rock under the monotonic uniaxial compression conditions,whereafter,the application of this model is extended to cyclic loading and unloading conditions.To validate the proposed monotonic and cyclic constitutive equations,a series of mechanical tests for marble specimens were carried out,which contained the monotonic uniaxial compression(MUC)experiment,cyclic uniaxial compression experiments under the variable amplitude(CUC-VA)and constant amplitude(CUC-CA)conditions.The results show that the proposed total damage variable comprehensively reflects the damage evolution characteristic,i.e.,the damage variable firstly decreases,then increases no matter under the conditions of MUC,CUC-VA or CUC-CA.Then a reasonable consistency is observed between the experimental and theoretical curves.The proposed cyclic constitutive equations can simulate the whole cyclic loading and unloading behaviors,such as the initial compaction,the strain hardening and the strain softening.Furthermore,the shapes of the theoretical curves are controlled by the modified coefficient,compaction sensitivity coefficient and two Weibull distributed parameters.
基金supported by the National Natural Science Foundation of China(51208031 and 51278047)the National Basic Research Program of China(2010CB732100)
文摘Thermo-Hydro-Mechanical （THM） coupling pro- cesses in unsaturated soils are very important in both theoretical researches and engineering applications. A coupled formulation based on hybrid mixture theory is derived to model the THM coupling behavior of unsaturated soils. The free-energy and dissipative functions for different phases are derived from Taylor＇s series expansions. Constitutive relations for THM coupled behaviors of unsaturated soils, which include deformation, entropy change, fluid flow, heat conduction, and dynamic compatibility conditions on the interfaces, are then established. The number of field equations is shown to be equal to the number of unknown variables; thus, a closure of this coupling problem is established. In addition to modifications of the physical conservation equations with coupling effect terms, the constitutive equations, which consider the coupling between elastoplastic deformation of the soil skeleton, fluid flow, and heat transfer, are also derived.
基金Project(KP200905) supports by the Fund of the State Key Laboratory of Solidification Processing in Northwestern Polytechnical University,China
文摘A constitutive equation was proposed to describe the effect of grain size on the deformation behavior.And a coupling simulation of deformation with heat transfer and microstructure was carried out in isothermal upsetting process of Ti60 alloy.The effects of processing parameters on the equivalent strain,the equivalent stress,the temperature rise and the grain size distribution in isothermal upsetting process of Ti60 alloy were analyzed.It is concluded that the uniformity of equivalent strain and equivalent stress increases with the increase of deformation temperature.However,the temperature rise and the grain size decreases with the increase of deformation temperature.The non-uniformity of equivalent strain,equivalent stress,temperature field and grain size increases with the increase of height reduction.And the calculated grain size using simulation is in good agreement with the experimental one.
文摘Elasto-plastic consolidation is one of the classic coupling questions in geomechanics. To solve this problem, an elasto-plastic constitutive model is derived based on the numerical modeling method. The model is applied to Blot＇s consolidation theory. Incremental governing partial differential equations are established using this method. According to the stress path, the decoupling condition of these equations is discussed. Based on these conditions, an incremental diffusion equation and uncoupling governing equations are presented. The method is then applied to numerical analyses of three examples. The results show that （1） the effect of the stress path should be taken into account in the simulation of the soil consolidation question; （2） this decoupling method can predict the evolvement of pore water pressure; （3） the settlement using cam-clay model is less than that using numerical model because of dilatancy.
文摘According to the prominent characteristic of rapid heating and cooling velocity in process of laser phase transformation hardening, it is important and necessary to consider the couple relation among temperature, phase transformation and stress. Based on the above, a mathematical model to analyze transformation and to reflect its characteristic is presented. Also temperature field control equation relative to stress and phase transformation is set up and thermal elastoplastic constitutive equation containing phase transformation was derived, In a given yield condition, temperature and stress field are numerically calculated by means of Finite Element Method. The result indicates the calculation value coincides with result of test Stress especially thermal stress varied violently in process of laser phase transformation hardening, which leaded to the residual stress on the surface and accorded to the fact. This process can improve the characteristic of material, so it is significant to study on thermal stress of laser quenching, to discuss the effect of phase transformation and stress on temperature, to optimize the laser quenching process and to improve the synthetic mechanic properties of quenching material.
