The mass entransy describes the mass-diffusion ability of the solution system, and the mass-diffusion process with the finite concentration difference always leads to the mass-entransy dissipation. This paper studies ...The mass entransy describes the mass-diffusion ability of the solution system, and the mass-diffusion process with the finite concentration difference always leads to the mass-entransy dissipation. This paper studies the equimolar reverse constant-temperature mass-diffusion process with Fick's law( g∝Δ(c)). The optimal concentration paths for the MED(Minimum Entransy Dissipation) are derived and compared with those for the MEG(Minimum Entropy Generation) and CCR(Constant Concentration Ratio) operations. It is indicated that the strategy of the MED is equivalent to that of the CCD(Constant Concentration Difference) of the same component; whether the MED or the MEG is selected as the optimization objective, the strategy of the CCD is much better than that of the CCR.展开更多
The hydrogen distribution of 16MnR steel weldment in hydrogen contained environment was calculated using the finite element method （ FEM）. The effect of welding residual stress on hydrogen diffusion has been discuss...The hydrogen distribution of 16MnR steel weldment in hydrogen contained environment was calculated using the finite element method （ FEM）. The effect of welding residual stress on hydrogen diffusion has been discussed using a 3-D sequential coupling finite element analysis procedure complied by Abaqus code. The hydrogen diffusion coefficient in weld metal, the heat affected zone （HAZ）, and the base metal of the 16MnR steel weldment were measured using the electrochemical permeation technique. The hydrogen diffusion without the effect of stress was also calculated and compared. Owing to the existence of welding residual stress, the hydrogen concentration was obviously increased and the hydrogen wouM diffuse and accumulate in the higher stress region.展开更多
An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix,which can be achieved by solving the advection-diffusion equation.Because of the directionality of the advection...An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix,which can be achieved by solving the advection-diffusion equation.Because of the directionality of the advection term,the discrete method needs to be chosen very carefully.The finite analytic method is an alternative scheme to solve the advection-diffusion equation.As a combination of analytical and numerical methods,it not only has high calculation accuracy but also holds the characteristic of the auto upwind.To demonstrate its ability,the one-dimensional steady and unsteady advection-diffusion equation numerical examples are respectively solved by the finite analytic method.The more widely used upwind difference method is used as a control approach.The result indicates that the finite analytic method has higher accuracy than the upwind difference method.For the two-dimensional case,the finite analytic method still has a better performance.In the three-dimensional variational assimilation experiment,the finite analytic method can effectively improve analysis field accuracy,and its effect is significantly better than the upwind difference and the central difference method.Moreover,it is still a more effective solution method in the strong flow region where the advective-diffusion filter performs most prominently.展开更多
The Perturbational Finite Difference (PFD) method is a kind of high-order-accurate compact difference method, but its idea is different from the normal compact method and the multi-nodes method. This method can get a ...The Perturbational Finite Difference (PFD) method is a kind of high-order-accurate compact difference method, but its idea is different from the normal compact method and the multi-nodes method. This method can get a Perturbational Exact Numerical Solution P(PENS) scheme for locally linearized Convection-Diffusion (CD) equation. The PENS scheme is similar to the Finite Analytical (FA) scheme and Exact Difference Solution (EDS) scheme, which are all exponential schemes, but PENS scheme is simpler and uses only 3,5 and 7 nodes for 1-, 2- and 3-dimensional problems, respectively. The various approximate schemes of PENs scheme are also called Perturbational-High-order-accurate Difference (PHD) scheme. The PHD schemes can be got by expanding the exponential terms in the PENS scheme into power series of grid Reynolds number, and they are all upwind schemes and remain the concise structure form of first-order upwind scheme. For 1-dimensional (1-D) CD equation and 2-D incompressible Navier-Stokes equation, their PENS and PHD schemes were constituted in this paper, they all gave highly accurate results for the numerical examples of three 1-D CD equations and an incompressible 2-D flow in a square cavity.展开更多
Magnesium alloys have shown great potential for their use in the medical device field, due to the promising biodegradability. However, it remains a challenge to characterize the degradation behavior of the Mg alloys i...Magnesium alloys have shown great potential for their use in the medical device field, due to the promising biodegradability. However, it remains a challenge to characterize the degradation behavior of the Mg alloys in a quantitative manner. As such, controlling the degradation rate of the Mg alloys as per our needs is still hard, which greatly limits the practical application of the Mg alloys as a degradable biomaterial.This paper discussed a numerical model developed based on the diffusion theory, which can capture the experimental degradation behavior of the Mg alloys precisely. The numerical model is then implemented into a finite element scheme, where the model is calibrated with the data from our previous studies on the corrosion of the as-cast Mg-1 Ca and the as-rolled Mg-3 Ge binary alloys. The degradation behavior of a pin implant is predicted using the calibrated model to demonstrate the model’s capability. A standard flow is provided in a practical framework for obtaining the degradation behavior of any biomedical Mg alloys. This methodology was further verified via the comparison with enormous available experimental results. Lastly, the material parameters defined in this model were provided as a new kind of material property.展开更多
Thermal self-compressing bonding(TSCB) is a new solid-state bonding method pioneered by the authors. With electron beam as the non-melted heat source, previous experimental study performed on titanium alloys has prove...Thermal self-compressing bonding(TSCB) is a new solid-state bonding method pioneered by the authors. With electron beam as the non-melted heat source, previous experimental study performed on titanium alloys has proved the feasibility of TSCB. However, the thermal stress–strain process during bonding, which is of very important significance in revealing the mechanism of TSCB, was not analysed. In this paper, finite element analysis method is adopted to numerically study the thermal elasto-plastic stress–strain cycle of thermal self-compressing bonding. It is found that due to the localized heating, a non-uniform temperature distribution is formed during bonding, with the highest temperature existed on the bond interface. The expansion of high temperature materials adjacent to the bond interface are restrained by surrounding cool materials and rigid restraints, and thus an internal elasto-plastic stress–strain field is developed by itself which makes the bond interface subjected to thermal compressive action. This thermal self-compressing action combined with the high temperature on the bond interface promotes the atom diffusion across the bond interface to produce solid-state joints. Due to the relatively large plastic deformation, rigid restraint TSCB obtains sound joints in relatively short time compared to diffusion bonding.展开更多
Based on the weak formulation for combined surface diffusion and evaporation-condensation,a governing equation of the finite element is derived for simulating the evolution of intergranular microcracks in copper inter...Based on the weak formulation for combined surface diffusion and evaporation-condensation,a governing equation of the finite element is derived for simulating the evolution of intergranular microcracks in copper interconnects induced simultaneously by stressmigration,electromigration and thermomigration.Unlike previously published works,the effect of thermomigration is considered.The results show that thermomigration can contribute to the microcrack splitting and accelerate the drifting process along the direction of the electric field.The evolution of the intergranular microcracks depends on the mechanical stress field,the temperature gradient field,the electric field,the initial aspect ratio and the linewidth.And there exists a critical electric fieldχ_c,a critical stress field■,a critical aspect ratioβ_c and a critical linewidth■.When■or■,the intergranular microcrack will split into two or three small intergranular microcracks.Otherwise,the microcrack will evolve into a stable shape as it migrates along the interconnect line.The critical stress field,the critical electric field and the critical aspect ratio decrease with a decrease in the linewidth,and the critical linewidth increases with an increase in the electric field and the aspect ratio.The increase of the stress field,the electric field or the aspect ratio and the decrease of the linewidth are not only beneficial for the intergranular microcrack to split but also accelerate the microcrack splitting process.展开更多
Lithium metal anode is one of the most important anode materials for next-generation high-specificenergy secondary batteries.Structured lithium metal anodes have received extensive attention in the development of prac...Lithium metal anode is one of the most important anode materials for next-generation high-specificenergy secondary batteries.Structured lithium metal anodes have received extensive attention in the development of practical lithium metal batteries.Methods of driving lithium metal to deposit inside the pores of structured lithium metal anodes have always been one of the most concerned issues,especially for highly conductive frameworks.An electrochemical phase field theory with galvanostatic lithium plating process is employed in this work,the mechanism that illustrates the preference of lithium metal to deposit at the top of the framework structure has been revealed,and through the simulation analysis of various regulating strategies,the strategies that can efficiently drive lithium to deposit inside structured pores are summarized.This work presents the theoretical calculation and analysis methods that can be used for the rational design of lithium metal batteries.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 51576207 & 51356001)
文摘The mass entransy describes the mass-diffusion ability of the solution system, and the mass-diffusion process with the finite concentration difference always leads to the mass-entransy dissipation. This paper studies the equimolar reverse constant-temperature mass-diffusion process with Fick's law( g∝Δ(c)). The optimal concentration paths for the MED(Minimum Entransy Dissipation) are derived and compared with those for the MEG(Minimum Entropy Generation) and CCR(Constant Concentration Ratio) operations. It is indicated that the strategy of the MED is equivalent to that of the CCD(Constant Concentration Difference) of the same component; whether the MED or the MEG is selected as the optimization objective, the strategy of the CCD is much better than that of the CCR.
文摘The hydrogen distribution of 16MnR steel weldment in hydrogen contained environment was calculated using the finite element method （ FEM）. The effect of welding residual stress on hydrogen diffusion has been discussed using a 3-D sequential coupling finite element analysis procedure complied by Abaqus code. The hydrogen diffusion coefficient in weld metal, the heat affected zone （HAZ）, and the base metal of the 16MnR steel weldment were measured using the electrochemical permeation technique. The hydrogen diffusion without the effect of stress was also calculated and compared. Owing to the existence of welding residual stress, the hydrogen concentration was obviously increased and the hydrogen wouM diffuse and accumulate in the higher stress region.
基金The National Key Research and Development Program of China under contract Nos 2022YFC3104804,2021YFC3101501,and 2017YFC1404103the National Programme on Global Change and Air-Sea Interaction of China under contract No.GASI-IPOVAI-04the National Natural Science Foundation of China under contract Nos 41876014,41606039,and 11801402.
文摘An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix,which can be achieved by solving the advection-diffusion equation.Because of the directionality of the advection term,the discrete method needs to be chosen very carefully.The finite analytic method is an alternative scheme to solve the advection-diffusion equation.As a combination of analytical and numerical methods,it not only has high calculation accuracy but also holds the characteristic of the auto upwind.To demonstrate its ability,the one-dimensional steady and unsteady advection-diffusion equation numerical examples are respectively solved by the finite analytic method.The more widely used upwind difference method is used as a control approach.The result indicates that the finite analytic method has higher accuracy than the upwind difference method.For the two-dimensional case,the finite analytic method still has a better performance.In the three-dimensional variational assimilation experiment,the finite analytic method can effectively improve analysis field accuracy,and its effect is significantly better than the upwind difference and the central difference method.Moreover,it is still a more effective solution method in the strong flow region where the advective-diffusion filter performs most prominently.
文摘The Perturbational Finite Difference (PFD) method is a kind of high-order-accurate compact difference method, but its idea is different from the normal compact method and the multi-nodes method. This method can get a Perturbational Exact Numerical Solution P(PENS) scheme for locally linearized Convection-Diffusion (CD) equation. The PENS scheme is similar to the Finite Analytical (FA) scheme and Exact Difference Solution (EDS) scheme, which are all exponential schemes, but PENS scheme is simpler and uses only 3,5 and 7 nodes for 1-, 2- and 3-dimensional problems, respectively. The various approximate schemes of PENs scheme are also called Perturbational-High-order-accurate Difference (PHD) scheme. The PHD schemes can be got by expanding the exponential terms in the PENS scheme into power series of grid Reynolds number, and they are all upwind schemes and remain the concise structure form of first-order upwind scheme. For 1-dimensional (1-D) CD equation and 2-D incompressible Navier-Stokes equation, their PENS and PHD schemes were constituted in this paper, they all gave highly accurate results for the numerical examples of three 1-D CD equations and an incompressible 2-D flow in a square cavity.
基金supported by National Key Research and Development Program of China (Grant No. 2016YFC1102402)National Natural Science Foundation of China (Grant No. 51431002 and 51871004)+1 种基金NSFC/RGC Joint Research Scheme (Grant No. 51661165014)Peking University Medicine Seed Fund for Interdisciplinary Research (Grant No. BMU2018ME005)
文摘Magnesium alloys have shown great potential for their use in the medical device field, due to the promising biodegradability. However, it remains a challenge to characterize the degradation behavior of the Mg alloys in a quantitative manner. As such, controlling the degradation rate of the Mg alloys as per our needs is still hard, which greatly limits the practical application of the Mg alloys as a degradable biomaterial.This paper discussed a numerical model developed based on the diffusion theory, which can capture the experimental degradation behavior of the Mg alloys precisely. The numerical model is then implemented into a finite element scheme, where the model is calibrated with the data from our previous studies on the corrosion of the as-cast Mg-1 Ca and the as-rolled Mg-3 Ge binary alloys. The degradation behavior of a pin implant is predicted using the calibrated model to demonstrate the model’s capability. A standard flow is provided in a practical framework for obtaining the degradation behavior of any biomedical Mg alloys. This methodology was further verified via the comparison with enormous available experimental results. Lastly, the material parameters defined in this model were provided as a new kind of material property.
基金Supported by National Natural Science Foundation of China(Grant No.51705491)
文摘Thermal self-compressing bonding(TSCB) is a new solid-state bonding method pioneered by the authors. With electron beam as the non-melted heat source, previous experimental study performed on titanium alloys has proved the feasibility of TSCB. However, the thermal stress–strain process during bonding, which is of very important significance in revealing the mechanism of TSCB, was not analysed. In this paper, finite element analysis method is adopted to numerically study the thermal elasto-plastic stress–strain cycle of thermal self-compressing bonding. It is found that due to the localized heating, a non-uniform temperature distribution is formed during bonding, with the highest temperature existed on the bond interface. The expansion of high temperature materials adjacent to the bond interface are restrained by surrounding cool materials and rigid restraints, and thus an internal elasto-plastic stress–strain field is developed by itself which makes the bond interface subjected to thermal compressive action. This thermal self-compressing action combined with the high temperature on the bond interface promotes the atom diffusion across the bond interface to produce solid-state joints. Due to the relatively large plastic deformation, rigid restraint TSCB obtains sound joints in relatively short time compared to diffusion bonding.
基金supported by the Natural Science Foundation of Jiangsu Province of China (No.BK20141407)the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Based on the weak formulation for combined surface diffusion and evaporation-condensation,a governing equation of the finite element is derived for simulating the evolution of intergranular microcracks in copper interconnects induced simultaneously by stressmigration,electromigration and thermomigration.Unlike previously published works,the effect of thermomigration is considered.The results show that thermomigration can contribute to the microcrack splitting and accelerate the drifting process along the direction of the electric field.The evolution of the intergranular microcracks depends on the mechanical stress field,the temperature gradient field,the electric field,the initial aspect ratio and the linewidth.And there exists a critical electric fieldχ_c,a critical stress field■,a critical aspect ratioβ_c and a critical linewidth■.When■or■,the intergranular microcrack will split into two or three small intergranular microcracks.Otherwise,the microcrack will evolve into a stable shape as it migrates along the interconnect line.The critical stress field,the critical electric field and the critical aspect ratio decrease with a decrease in the linewidth,and the critical linewidth increases with an increase in the electric field and the aspect ratio.The increase of the stress field,the electric field or the aspect ratio and the decrease of the linewidth are not only beneficial for the intergranular microcrack to split but also accelerate the microcrack splitting process.
基金supported by Beijing Natural Science Foundation(JQ20004)National Key Research and Development Program(2021YFB2400300)+1 种基金National Natural Scientific Foundation of China(22109011)the China Postdoctoral Science Foundation(BX20200047,2021M690380)。
文摘Lithium metal anode is one of the most important anode materials for next-generation high-specificenergy secondary batteries.Structured lithium metal anodes have received extensive attention in the development of practical lithium metal batteries.Methods of driving lithium metal to deposit inside the pores of structured lithium metal anodes have always been one of the most concerned issues,especially for highly conductive frameworks.An electrochemical phase field theory with galvanostatic lithium plating process is employed in this work,the mechanism that illustrates the preference of lithium metal to deposit at the top of the framework structure has been revealed,and through the simulation analysis of various regulating strategies,the strategies that can efficiently drive lithium to deposit inside structured pores are summarized.This work presents the theoretical calculation and analysis methods that can be used for the rational design of lithium metal batteries.
