The particle simulation method is used to solve free-surface slurry flow problems that may be encountered in several scientific and engineering fields.The main idea behind the use of the particle simulation method is ...The particle simulation method is used to solve free-surface slurry flow problems that may be encountered in several scientific and engineering fields.The main idea behind the use of the particle simulation method is to treat granular or other materials as an assembly of many particles.Compared with the continuum-mechanics-based numerical methods such as the finite element and finite volume methods,the movement of each particle is accurately described in the particle simulation method so that the free surface of a slurry flow problem can be automatically obtained.The major advantage of using the particle simulation method is that only a simple numerical algorithm is needed to solve the governing equation of a particle simulation system.For the purpose of illustrating how to use the particle simulation method to solve free-surface flow problems,three examples involving slurry flow on three different types of river beds have been considered.The related particle simulation results obtained from these three examples have demonstrated that:1) The particle simulation method is a promising and useful method for solving free-surface flow problems encountered in both the scientific and engineering fields;2) The shape and irregular roughness of a river bed can have a significant effect on the free surface morphologies of slurry flow when it passes through the river bed.展开更多
A mine-scale analysis of Longwall Top Coal Caving (LTCC) is performed using a continuum mechanics finite element solver called COSFLOW. The uniqueness of COSFLOW is that it incorporates Cosserat continuum theory in it...A mine-scale analysis of Longwall Top Coal Caving (LTCC) is performed using a continuum mechanics finite element solver called COSFLOW. The uniqueness of COSFLOW is that it incorporates Cosserat continuum theory in its formulation for describing the load deformation of bedded rocks. It is shown that such a continuum based code is valuable for assessing the feasibility of introducing LTCC in any mine. Various LTCC parameters, for example chock convergences, top coal failure behavior, strata cavingmechanism, abutment stresses and vertical stresses, were evaluated for a mine using COSFLOW.展开更多
From the continuum mechanics perspective, an attempt was made to clarify the role of Terzaghi's effective stress in the theoretical analysis of saturated soil subjected to seepage. The necessity of performing a co...From the continuum mechanics perspective, an attempt was made to clarify the role of Terzaghi's effective stress in the theoretical analysis of saturated soil subjected to seepage. The necessity of performing a coupled hydromechanical analysis to solve the seepage-deformation interaction problem was illustrated by examining the equations of static equilibrium among the effective stress, seepage force, pore-water pressure and total stress. The conceptual definition of stress variable that satisfies the principles of continuum mechanics is applied in the coupled hydromechanical analysis. It is shown that Terzaghi's effective stress is in fact not a stress variable under seepage conditions, and the seepage force acting on the soil skeleton cannot be viewed as a body force. This offers a clue to the underlying cause of a paradox between the real Pascal's hydrostatic state and the hydrostatic state predicted by a class of continuum hydromechanical theories.展开更多
A mechanical structure of space is suggested. On the supposition that a space as vacuum has a physical fine structure like continuum, it enables us to apply a continuum mechanics to the so-called ＂vacuum＂ of space. ...A mechanical structure of space is suggested. On the supposition that a space as vacuum has a physical fine structure like continuum, it enables us to apply a continuum mechanics to the so-called ＂vacuum＂ of space. A space is an infinite continuum and its structure is determined by Riemannian geometry. Assuming that space is an infmite continuum, the pressure field derived from the geometrical structure of space is newly obtained by applying both continuum mechanics and General Relativity to space. A fundamental concept of space-time is described that focuses on theoretically innate properties of space including strain and curvature. As a trial consideration, gravity can be explained as a pressure field induced by the curvature of space.展开更多
Various numerical methods are available to model,simulate,analyse and interpret the results;however a major task is to select a reliable and intended tool to perform a realistic assessment of any problem.For a model t...Various numerical methods are available to model,simulate,analyse and interpret the results;however a major task is to select a reliable and intended tool to perform a realistic assessment of any problem.For a model to be a representative of the realistic mining scenario,a verified tool must be chosen to perform an assessment of mine roof support requirement and address the geotechnical risks associated with longwall mining.The dependable tools provide a safe working environment,increased production,efficient management of resources and reduce environmental impacts of mining.Although various methods,for example,analytical,experimental and empirical are being adopted in mining,in recent days numerical tools are becoming popular due to the advancement in computer hardware and numerical methods.Empirical rules based on past experiences do provide a general guide,however due to the heterogeneous nature of mine geology(i.e.,none of the mine sites are identical),numerical simulations of mine site specific conditions would lend better insights into some underlying issues.The paper highlights the use of a continuum mechanics based tool in coal mining with a mine scale model.The continuum modelling can provide close to accurate stress fields and deformation.The paper describes the use of existing mine data to calibrate and validate the model parameters,which then are used to assess geotechnical issues related with installing a new high capacity longwall mine at the mine site.A variety of parameters,for example,chock convergences,caveability of overlying sandstones,abutment and vertical stresses have been estimated.展开更多
The continuous mediums are divided into two kinds according to their geometrical configurations,the first one is related to Euclidian manifolds and the other one to Riemannian manifolds/surfaces in the point of view o...The continuous mediums are divided into two kinds according to their geometrical configurations,the first one is related to Euclidian manifolds and the other one to Riemannian manifolds/surfaces in the point of view of the modern geometry.Two kinds of finite deformation theories with respect to Euclidian and Riemannian manifolds have been developed in the present paper.Both kinds of theories include the definitions of initial and current physical and parametric configurations,deformation gradient tensors with properties,deformation descriptions,transport theories and governing equations of nature conservation laws.The essential property of the theory with respect to Euclidian manifolds is that the curvilinear coordinates corresponding to the current physical configurations include time explicitly through which the geometrically irregular and time varying physical configurations can be mapped in the diffeomorphism manner to the regular and fixed domains in the parametric space.It is quite essential to the study of the relationships between geometries and mechanics.The theory with respect to Riemannian manifolds provides the systemic ideas and methods to study the deformations of continuous mediums whose geometrical configurations can be considered as general surfaces.The essential property of the theory with respect to Riemannian manifolds is that the thickness variation of a patch of continuous medium is represented by the surface density and its governing equation is rigorously deduced.As some applications,wakes of cylinders with deformable boundaries on the plane,incompressible wakes of a circular cylinder on fixed surfaces and axisymmetric finite deformations of an elastic membrane are numerically studied.展开更多
In this study,we considered the wetting phenomenon on a general substrate from a new viewpoint of continuum mechanics.The analyses first show how the Wenzel and the Cassie models deviate the practical results in some ...In this study,we considered the wetting phenomenon on a general substrate from a new viewpoint of continuum mechanics.The analyses first show how the Wenzel and the Cassie models deviate the practical results in some special substrates,and then elucidate the mechanism of the triple contact line(TCL) moving.Based upon variational theory of the total free functional dealing with the movable boundary condition,we show that the macroscopic contact angle(MCA) expression is the corresponding transversality condition.It manifests that the MCA depends only on the chemical and geometric property at the TCL,and is not affected by the gravity of the droplet and the contact area beneath the liquid.Our continuum model also shows the exploration of the pinning effect on a sharp wedge or the interface between two different phases.This investigation will help designing super-hydrophobic materials for novel micro-fluidic devices.展开更多
Continuum mechanics, just as the name implies, deals with the mechanics problems of all continua, whose physical （or mechanical） properties are assumed to vary continuously in the spaces they occupy. Continuum mecha...Continuum mechanics, just as the name implies, deals with the mechanics problems of all continua, whose physical （or mechanical） properties are assumed to vary continuously in the spaces they occupy. Continuum mechanics may be seen as the symbol of modem mechanics, which differs greatly from current physics, the two often being mixed up by people and even sci- entists. In this short paper, I will first try to give an illustration on the differences between （modem） mechanics and physics, in my personal view, and then focus on some important current research activities in continuum mechanics, attempting to identify its path to the near future. We can see that continuum mechanics, while having a dominating impact on engineering design in the 20th century, also plays a pivotal role in modem science, and is much closer to physics, chemistry, biology, etc. than ever before.展开更多
A consistent focus in theoretical mechanics has been on how to apply Lagrange's equation to continuum mechanics.This paper uses the concept of a variational derivative and its laws of operation to investigate the ...A consistent focus in theoretical mechanics has been on how to apply Lagrange's equation to continuum mechanics.This paper uses the concept of a variational derivative and its laws of operation to investigate the derivation of Lagrange's equation,which is then applied to nonlinear elasto-dynamics.In accordance with the work-energy principle and the energy conservation law,kinetic and potential energies are proposed for rigid-elastic coupling dynamics,whose governing equation is established by manipulating Lagrange's equation.In addition,case studies are used to demonstrate the application of the proposed method to spacecraft dynamics.展开更多
The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, the...The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, thermal-electrical change, surrounding elastic medium and the Van der Waals forces are all taken into consideration. The governing equation of buckling for CNTs subjected to thermo-electro-mechanical loadings has been established based on an elastic shell model of continuum mechanics. Reasonable simplifications are made to get the explicit expression of the critical buckling shear stress of DWCNTs, and numerical experiments are conducted for further research. It is shown that under certain electric and temperature field the critical buckling shear stress of DWCNTs only depends on the wave number of buckling modes. On the other hand, all the related impact factors have enormous influence on the critical buckling shear stress under a certain buckling mode. The critical buckling shear stress changes linearly with the axial-to-shear stress ratio, as well as the thermal and electric change. Axial compression tends to make DWCNTs unstable, while axial tension benefits the buckling stability. The critical buckling shear stress is directly proportional to the applied voltage. At room or lower temperature, the critical shear stress for infinitesimal buckling increases as the temperature change increases, while it decreases at a higher temperature. The conclusions are useful for the design of nano-structures related to the buckling stability of DWCNTs.展开更多
In this paper,a new dynamic model for the flexible hub-beam system is proposed by using the principle of continuum medium mechanics and the finite element discretization method.In the proposed model,the coupling defor...In this paper,a new dynamic model for the flexible hub-beam system is proposed by using the principle of continuum medium mechanics and the finite element discretization method.In the proposed model,the coupling deformation of any element of the beam is only related with the nodal coordinates of this element.So this model is suitable to the rotating beam in an arbitrary shape.Numerical examples of slender beams in straight and irregular shapes are carried out to demonstrate the validation of the proposed model.Simulation results indicate that the proposed model can be used valid for dynamic description of flexible rotating beam in irregular shape, and for both low and high rotation speeds.展开更多
This paper presents a macroscopic constitutive model reproducing the hysteretic behaviors of the superelastic shape memory alloy (SMA) under cyclic loading. The progressive increase of residual strain with the increas...This paper presents a macroscopic constitutive model reproducing the hysteretic behaviors of the superelastic shape memory alloy (SMA) under cyclic loading. The progressive increase of residual strain with the increased cycle number in such materials is assumed to be a consequence of the progressive increase of residual stress-induced martensitic volume fraction upon the cyclic effects. The progressive decrease of phase transformation critical stresses with the increased cycle number in such materials is assumed to be a result from the progressive increase of phase transformation critical temperatures upon the cyclic effects. A cyclic evolution equation is supposed to describe the influences of cycle effects on the material properties of the SMA under cyclic loading. A phase transformation equation expressing the phase transformation behaviors of the SMA under cyclic loading is established based on the differential relationship between martensitic volume fraction and the free energy increment of phase transformation. A mechanical constitutive equation predicting the mechanical characteristics of the SMA under cyclic loading is developed on the basis of thermodynamics and continuum mechanics. The cyclic evolution equation, phase transformation equation, and mechanical constitutive equation together compose the presented macroscopic constitutive model considering cyclic effects. Results of the numerical simulations illustrate that it can well reproduce the superelastic hysteretic behaviors of the SMA under cyclic loading.展开更多
We present in this paper a numerical algorithm that couples the atomistic and continuum models for the thermal-mechanical coupled problem of polycrystalline aggregates.The key point is that the conservation laws shoul...We present in this paper a numerical algorithm that couples the atomistic and continuum models for the thermal-mechanical coupled problem of polycrystalline aggregates.The key point is that the conservation laws should be satisfied for both the atomistic and continuum models at the microscale.Compared with the traditional methods which construct the constitutive equations of the grain interiors and grain boundaries by continuum mechanics,our model calculates the continuum fluxes through molecular dynamics simulations,provided that the atomistic simulations are consistent with the local microstate of the system.For the grain interiors without defects,central schemes are available for solving the conservation laws and the constitutive parameters can be obtained via molecular dynamics simulations.For the grain boundary structures,the front tracking method is employed because the solutions of the conservation equations are discontinuous near the defects.Firstly,appropriate control volumes are chosen at both sides of the interface,then the finite volume method is applied to solve the continuum equations in each control volume.Fluxes near both sides of the interface are calculated via atomistic simulations.Therefore,all thermo-mechanical information can be obtained.展开更多
基金Project(11272359)supported by the National Natural Science Foundation of China
文摘The particle simulation method is used to solve free-surface slurry flow problems that may be encountered in several scientific and engineering fields.The main idea behind the use of the particle simulation method is to treat granular or other materials as an assembly of many particles.Compared with the continuum-mechanics-based numerical methods such as the finite element and finite volume methods,the movement of each particle is accurately described in the particle simulation method so that the free surface of a slurry flow problem can be automatically obtained.The major advantage of using the particle simulation method is that only a simple numerical algorithm is needed to solve the governing equation of a particle simulation system.For the purpose of illustrating how to use the particle simulation method to solve free-surface flow problems,three examples involving slurry flow on three different types of river beds have been considered.The related particle simulation results obtained from these three examples have demonstrated that:1) The particle simulation method is a promising and useful method for solving free-surface flow problems encountered in both the scientific and engineering fields;2) The shape and irregular roughness of a river bed can have a significant effect on the free surface morphologies of slurry flow when it passes through the river bed.
文摘A mine-scale analysis of Longwall Top Coal Caving (LTCC) is performed using a continuum mechanics finite element solver called COSFLOW. The uniqueness of COSFLOW is that it incorporates Cosserat continuum theory in its formulation for describing the load deformation of bedded rocks. It is shown that such a continuum based code is valuable for assessing the feasibility of introducing LTCC in any mine. Various LTCC parameters, for example chock convergences, top coal failure behavior, strata cavingmechanism, abutment stresses and vertical stresses, were evaluated for a mine using COSFLOW.
基金Project(51278171)supported by the National Natural Science Foundation of ChinaProject(B13024)supported by the"111"Project,China+1 种基金Projects(2014B04914,2011B02814,2010B28114)supported by the Fundamental Research Funds for the Central Universities of ChinaProject(617608)supported by the Research Grants Council of the Hong Kong Special Administrative Region of China
文摘From the continuum mechanics perspective, an attempt was made to clarify the role of Terzaghi's effective stress in the theoretical analysis of saturated soil subjected to seepage. The necessity of performing a coupled hydromechanical analysis to solve the seepage-deformation interaction problem was illustrated by examining the equations of static equilibrium among the effective stress, seepage force, pore-water pressure and total stress. The conceptual definition of stress variable that satisfies the principles of continuum mechanics is applied in the coupled hydromechanical analysis. It is shown that Terzaghi's effective stress is in fact not a stress variable under seepage conditions, and the seepage force acting on the soil skeleton cannot be viewed as a body force. This offers a clue to the underlying cause of a paradox between the real Pascal's hydrostatic state and the hydrostatic state predicted by a class of continuum hydromechanical theories.
文摘A mechanical structure of space is suggested. On the supposition that a space as vacuum has a physical fine structure like continuum, it enables us to apply a continuum mechanics to the so-called ＂vacuum＂ of space. A space is an infinite continuum and its structure is determined by Riemannian geometry. Assuming that space is an infmite continuum, the pressure field derived from the geometrical structure of space is newly obtained by applying both continuum mechanics and General Relativity to space. A fundamental concept of space-time is described that focuses on theoretically innate properties of space including strain and curvature. As a trial consideration, gravity can be explained as a pressure field induced by the curvature of space.
基金the Asia Pacific Partnership and the Singareni Collieries Company Ltd
文摘Various numerical methods are available to model,simulate,analyse and interpret the results;however a major task is to select a reliable and intended tool to perform a realistic assessment of any problem.For a model to be a representative of the realistic mining scenario,a verified tool must be chosen to perform an assessment of mine roof support requirement and address the geotechnical risks associated with longwall mining.The dependable tools provide a safe working environment,increased production,efficient management of resources and reduce environmental impacts of mining.Although various methods,for example,analytical,experimental and empirical are being adopted in mining,in recent days numerical tools are becoming popular due to the advancement in computer hardware and numerical methods.Empirical rules based on past experiences do provide a general guide,however due to the heterogeneous nature of mine geology(i.e.,none of the mine sites are identical),numerical simulations of mine site specific conditions would lend better insights into some underlying issues.The paper highlights the use of a continuum mechanics based tool in coal mining with a mine scale model.The continuum modelling can provide close to accurate stress fields and deformation.The paper describes the use of existing mine data to calibrate and validate the model parameters,which then are used to assess geotechnical issues related with installing a new high capacity longwall mine at the mine site.A variety of parameters,for example,chock convergences,caveability of overlying sandstones,abutment and vertical stresses have been estimated.
基金supported by the National Nature Science Foundation of China (Grant Nos. 11172069 and 10872051)some key project of education reforms issued by the Shanghai Municipal Education Commission (2011)
文摘The continuous mediums are divided into two kinds according to their geometrical configurations,the first one is related to Euclidian manifolds and the other one to Riemannian manifolds/surfaces in the point of view of the modern geometry.Two kinds of finite deformation theories with respect to Euclidian and Riemannian manifolds have been developed in the present paper.Both kinds of theories include the definitions of initial and current physical and parametric configurations,deformation gradient tensors with properties,deformation descriptions,transport theories and governing equations of nature conservation laws.The essential property of the theory with respect to Euclidian manifolds is that the curvilinear coordinates corresponding to the current physical configurations include time explicitly through which the geometrically irregular and time varying physical configurations can be mapped in the diffeomorphism manner to the regular and fixed domains in the parametric space.It is quite essential to the study of the relationships between geometries and mechanics.The theory with respect to Riemannian manifolds provides the systemic ideas and methods to study the deformations of continuous mediums whose geometrical configurations can be considered as general surfaces.The essential property of the theory with respect to Riemannian manifolds is that the thickness variation of a patch of continuous medium is represented by the surface density and its governing equation is rigorously deduced.As some applications,wakes of cylinders with deformable boundaries on the plane,incompressible wakes of a circular cylinder on fixed surfaces and axisymmetric finite deformations of an elastic membrane are numerically studied.
基金supported by the National Natural Science Foundation of China(Grant Nos.10802099,11272357 and 11102140)the Doctoral Fund of Ministry of Education of China(Grant No.20110141120024)+2 种基金the Natural Science Foundation of Shandong Province(Grant No.ZR2009AQ006)the Opening Project of State Key Laboratory of Explosion Science and Technology(Beijing Institute of Technology)(Grant No. KFJJ12-11M)the support from the Brain Korea 21 Program at Seoul National University
文摘In this study,we considered the wetting phenomenon on a general substrate from a new viewpoint of continuum mechanics.The analyses first show how the Wenzel and the Cassie models deviate the practical results in some special substrates,and then elucidate the mechanism of the triple contact line(TCL) moving.Based upon variational theory of the total free functional dealing with the movable boundary condition,we show that the macroscopic contact angle(MCA) expression is the corresponding transversality condition.It manifests that the MCA depends only on the chemical and geometric property at the TCL,and is not affected by the gravity of the droplet and the contact area beneath the liquid.Our continuum model also shows the exploration of the pinning effect on a sharp wedge or the interface between two different phases.This investigation will help designing super-hydrophobic materials for novel micro-fluidic devices.
基金Project supported by the National Natural Science of Foundation of China(Nos.11321202 and 11272281)
文摘Continuum mechanics, just as the name implies, deals with the mechanics problems of all continua, whose physical （or mechanical） properties are assumed to vary continuously in the spaces they occupy. Continuum mechanics may be seen as the symbol of modem mechanics, which differs greatly from current physics, the two often being mixed up by people and even sci- entists. In this short paper, I will first try to give an illustration on the differences between （modem） mechanics and physics, in my personal view, and then focus on some important current research activities in continuum mechanics, attempting to identify its path to the near future. We can see that continuum mechanics, while having a dominating impact on engineering design in the 20th century, also plays a pivotal role in modem science, and is much closer to physics, chemistry, biology, etc. than ever before.
基金supported by the National Natural Science Foundation of China(Grant No.10272034)
文摘A consistent focus in theoretical mechanics has been on how to apply Lagrange's equation to continuum mechanics.This paper uses the concept of a variational derivative and its laws of operation to investigate the derivation of Lagrange's equation,which is then applied to nonlinear elasto-dynamics.In accordance with the work-energy principle and the energy conservation law,kinetic and potential energies are proposed for rigid-elastic coupling dynamics,whose governing equation is established by manipulating Lagrange's equation.In addition,case studies are used to demonstrate the application of the proposed method to spacecraft dynamics.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10902040, A020602)the Specialized Research Fund for the Doctoral Program of Higher Education(New Teachers)+2 种基金the Foundation for Distinguished Young Talents in Higher Education of Guangdong(Grant No. LYM08016)the Foundation for Outstanding Doctoral Dissertation of Guangdongthe Fundamental Research Funds for the Central Universities, South China University of Technology (Grant Nos.2009ZM0238,2009ZM0280)
文摘The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, thermal-electrical change, surrounding elastic medium and the Van der Waals forces are all taken into consideration. The governing equation of buckling for CNTs subjected to thermo-electro-mechanical loadings has been established based on an elastic shell model of continuum mechanics. Reasonable simplifications are made to get the explicit expression of the critical buckling shear stress of DWCNTs, and numerical experiments are conducted for further research. It is shown that under certain electric and temperature field the critical buckling shear stress of DWCNTs only depends on the wave number of buckling modes. On the other hand, all the related impact factors have enormous influence on the critical buckling shear stress under a certain buckling mode. The critical buckling shear stress changes linearly with the axial-to-shear stress ratio, as well as the thermal and electric change. Axial compression tends to make DWCNTs unstable, while axial tension benefits the buckling stability. The critical buckling shear stress is directly proportional to the applied voltage. At room or lower temperature, the critical shear stress for infinitesimal buckling increases as the temperature change increases, while it decreases at a higher temperature. The conclusions are useful for the design of nano-structures related to the buckling stability of DWCNTs.
基金the National Natural Science Foundationof China(Nos.10772113,10772112)
文摘In this paper,a new dynamic model for the flexible hub-beam system is proposed by using the principle of continuum medium mechanics and the finite element discretization method.In the proposed model,the coupling deformation of any element of the beam is only related with the nodal coordinates of this element.So this model is suitable to the rotating beam in an arbitrary shape.Numerical examples of slender beams in straight and irregular shapes are carried out to demonstrate the validation of the proposed model.Simulation results indicate that the proposed model can be used valid for dynamic description of flexible rotating beam in irregular shape, and for both low and high rotation speeds.
基金supported by the Fundamental Research Funds for Central Universities of China (Grant Nos. HEUCFZ1004, HEUCF110202 andHEUCF110204)the Harbin Talent Foundation of Scientific and Technical Innovation of China (Grant No. RC2009QN0170046)+1 种基金the Foundation for Returned Overseas Scholars from the Ministry of Education of China (Series 37)the National Postdoctoral Science Foundation of China(Grant No. 20080430933)
文摘This paper presents a macroscopic constitutive model reproducing the hysteretic behaviors of the superelastic shape memory alloy (SMA) under cyclic loading. The progressive increase of residual strain with the increased cycle number in such materials is assumed to be a consequence of the progressive increase of residual stress-induced martensitic volume fraction upon the cyclic effects. The progressive decrease of phase transformation critical stresses with the increased cycle number in such materials is assumed to be a result from the progressive increase of phase transformation critical temperatures upon the cyclic effects. A cyclic evolution equation is supposed to describe the influences of cycle effects on the material properties of the SMA under cyclic loading. A phase transformation equation expressing the phase transformation behaviors of the SMA under cyclic loading is established based on the differential relationship between martensitic volume fraction and the free energy increment of phase transformation. A mechanical constitutive equation predicting the mechanical characteristics of the SMA under cyclic loading is developed on the basis of thermodynamics and continuum mechanics. The cyclic evolution equation, phase transformation equation, and mechanical constitutive equation together compose the presented macroscopic constitutive model considering cyclic effects. Results of the numerical simulations illustrate that it can well reproduce the superelastic hysteretic behaviors of the SMA under cyclic loading.
基金supported by the National Basic Research Program of China (Grant No. 2010CB832702)the National Natural Science Foundation of China (Grant Nos. 90916027 and 11202065)
文摘We present in this paper a numerical algorithm that couples the atomistic and continuum models for the thermal-mechanical coupled problem of polycrystalline aggregates.The key point is that the conservation laws should be satisfied for both the atomistic and continuum models at the microscale.Compared with the traditional methods which construct the constitutive equations of the grain interiors and grain boundaries by continuum mechanics,our model calculates the continuum fluxes through molecular dynamics simulations,provided that the atomistic simulations are consistent with the local microstate of the system.For the grain interiors without defects,central schemes are available for solving the conservation laws and the constitutive parameters can be obtained via molecular dynamics simulations.For the grain boundary structures,the front tracking method is employed because the solutions of the conservation equations are discontinuous near the defects.Firstly,appropriate control volumes are chosen at both sides of the interface,then the finite volume method is applied to solve the continuum equations in each control volume.Fluxes near both sides of the interface are calculated via atomistic simulations.Therefore,all thermo-mechanical information can be obtained.
