Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical...Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.展开更多
Frank’s theory describes that a screw dislocation will produce a pit on the surface,and has been evidenced in many material systems including GaN.However,the size of the pit calculated from the theory deviates signif...Frank’s theory describes that a screw dislocation will produce a pit on the surface,and has been evidenced in many material systems including GaN.However,the size of the pit calculated from the theory deviates significantly from experimental result.Through a careful observation of the variations of surface pits and local surface morphology with growing temperature and V/III ratio for c-plane GaN,we believe that Frank’s model is valid only in a small local surface area where thermodynamic equilibrium state can be assumed to stay the same.If the kinetic process is too vigorous or too slow to reach a balance,the local equilibrium range will be too small for the center and edge of the screw dislocation spiral to be kept in the same equilibrium state.When the curvature at the center of the dislocation core reaches the critical value 1/r0,at the edge of the spiral,the accelerating rate of the curvature may not fall to zero,so the pit cannot reach a stationary shape and will keep enlarging under the control of minimization of surface energy to result in a large-sized surface pit.展开更多
In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics,shear bands in sand are considered as high-strain phase(plastic phase) of sand and the materials out...In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics,shear bands in sand are considered as high-strain phase(plastic phase) of sand and the materials outside the bands are still in low-strain phase(elastic phase),namely,the two phases of sand can coexist under certain condition.As a one-dimensional example,the results show that,for materials with strain-softening behavior,the two-phase solution is a stable branch of solutions,but the method to find two-phase solutions is very different from the one for bifurcation analysis.The theory of multi-phase equilibrium and the slow plastic flow model are applied to predict the formation and patterns of shear bands in sand specimens,discontinuity of deformation gradient and stress across interfaces between shear bands and other regions is considered,the continuity of displacements and traction across interfaces is imposed,and the Maxwell relation is satisfied.The governing equations are deduced.The critical stress for the formation of a shear band,both the stresses and strains inside the band and outside the band,and the inclination angle of the band can all be predicted.The predicted results are consistent with experimental measurements.展开更多
The existing magnetomechancial models cannot explain the different experimental phenomena when the ferromagnetic specimen is respectively subjected to tension and compression stress in the constant and low intensity m...The existing magnetomechancial models cannot explain the different experimental phenomena when the ferromagnetic specimen is respectively subjected to tension and compression stress in the constant and low intensity magnetic field,especially in the compression case. To promote the development of magnetomechancial theory, the energy conservation equation, effective magnetic field equation, and anhysteretic magnetization equation of the original Jiles-Atherton（J-A）theory are elucidated and modified, an equation of the local equilibrium status is employed and the differential expression of the modified magnetomechancial model based on the modified J-A theory is established finally. The effect of stress and plastic deformation on the magnetic parameters is analyzed. An excellent agreement is achieved between the theoretic predictions by the present modified model and the previous experimental results. Comparing with the calculation results given by the existing models and experimental results, it is seen indeed that the modified magnetomechanical model can describe the different magnetization features during tension-release and compression-release processes much better, and is the only one which can accurately reflect the experimental observation that the magnetic induction intensity reverses to negative value with the increase of the compressive stress and applied field.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10272070)and the Development Foun-dation of the Education Commission of Shanghai,China.
文摘Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11204009 and 61204011)the Beijing Municipal Natural Science Foundation,China(Grant No.4142005)
文摘Frank’s theory describes that a screw dislocation will produce a pit on the surface,and has been evidenced in many material systems including GaN.However,the size of the pit calculated from the theory deviates significantly from experimental result.Through a careful observation of the variations of surface pits and local surface morphology with growing temperature and V/III ratio for c-plane GaN,we believe that Frank’s model is valid only in a small local surface area where thermodynamic equilibrium state can be assumed to stay the same.If the kinetic process is too vigorous or too slow to reach a balance,the local equilibrium range will be too small for the center and edge of the screw dislocation spiral to be kept in the same equilibrium state.When the curvature at the center of the dislocation core reaches the critical value 1/r0,at the edge of the spiral,the accelerating rate of the curvature may not fall to zero,so the pit cannot reach a stationary shape and will keep enlarging under the control of minimization of surface energy to result in a large-sized surface pit.
基金Project(2007CB714001) supported by the National Basic Research Program of China (973 Program)
文摘In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics,shear bands in sand are considered as high-strain phase(plastic phase) of sand and the materials outside the bands are still in low-strain phase(elastic phase),namely,the two phases of sand can coexist under certain condition.As a one-dimensional example,the results show that,for materials with strain-softening behavior,the two-phase solution is a stable branch of solutions,but the method to find two-phase solutions is very different from the one for bifurcation analysis.The theory of multi-phase equilibrium and the slow plastic flow model are applied to predict the formation and patterns of shear bands in sand specimens,discontinuity of deformation gradient and stress across interfaces between shear bands and other regions is considered,the continuity of displacements and traction across interfaces is imposed,and the Maxwell relation is satisfied.The governing equations are deduced.The critical stress for the formation of a shear band,both the stresses and strains inside the band and outside the band,and the inclination angle of the band can all be predicted.The predicted results are consistent with experimental measurements.
基金Project supported by the Major Program of Sichuan Province Science and Technology Plan,China(Grant No.2015SZ0010)the Scientific Research Foundation of Sichuan Province,China(Grant No.2014GZ0121)
文摘The existing magnetomechancial models cannot explain the different experimental phenomena when the ferromagnetic specimen is respectively subjected to tension and compression stress in the constant and low intensity magnetic field,especially in the compression case. To promote the development of magnetomechancial theory, the energy conservation equation, effective magnetic field equation, and anhysteretic magnetization equation of the original Jiles-Atherton（J-A）theory are elucidated and modified, an equation of the local equilibrium status is employed and the differential expression of the modified magnetomechancial model based on the modified J-A theory is established finally. The effect of stress and plastic deformation on the magnetic parameters is analyzed. An excellent agreement is achieved between the theoretic predictions by the present modified model and the previous experimental results. Comparing with the calculation results given by the existing models and experimental results, it is seen indeed that the modified magnetomechanical model can describe the different magnetization features during tension-release and compression-release processes much better, and is the only one which can accurately reflect the experimental observation that the magnetic induction intensity reverses to negative value with the increase of the compressive stress and applied field.
