In this paper,an atom-continuum coupled model for thermo-mechanical behaviors in micro-nano scales is presented.A representative volume element consisting of atom clusters is used to represent the microstructure of ma...In this paper,an atom-continuum coupled model for thermo-mechanical behaviors in micro-nano scales is presented.A representative volume element consisting of atom clusters is used to represent the microstructure of materials.The atom motions in the RVE are divided into two phases,structural deformations and thermal vibrations.For the structural deformations,nonlinear and nonlocal deformation at atomic scales is considered.The atomistic-continuum equations are constructed based on momentum and energy conservation law.The non-locality and nonlinearity of atomistic interactions are built into the thermo-mechanical constitutive equations.The coupled atomistic-continuum thermal-mechanical simulation process is also suggested in this work.展开更多
H61der and gradient estimates for the correctors in the homogenization are presented based on the translation invariance and Li-Vogelius's gradient estimate. If the coefficients are piecewise smooth and the homogeniz...H61der and gradient estimates for the correctors in the homogenization are presented based on the translation invariance and Li-Vogelius's gradient estimate. If the coefficients are piecewise smooth and the homogenized solution is smooth enough, the interior error of the first-order expansion is O(e) in the HSlder norm; it is O(e) in W1,∞ based on the Avellaneda-Lin's gradient estimate when the coefficients are Lipschitz continuous. These estimates can be partly extended to the nonlinear parabolic equations.展开更多
This paper considers the bending behaviors of composite plate with 3-D periodic configuration.A second-order two-scale(SOTS)computational method is designed by means of construction way.First,by 3-D elastic composite ...This paper considers the bending behaviors of composite plate with 3-D periodic configuration.A second-order two-scale(SOTS)computational method is designed by means of construction way.First,by 3-D elastic composite plate model,the cell functions which are defined on the reference cell are constructed.Then the effective homogenization parameters of composites are calculated,and the homogenized plate problem on original domain is defined.Based on the Reissner-Mindlin deformation pattern,the homogenization solution is obtained.And then the SOTS’s approximate solution is obtained by the cell functions and the homogenization solution.Second,the approximation of the SOTS’s solution in energy norm is analyzed and the residual of SOTS’s solution for 3-D original in the pointwise sense is investigated.Finally,the procedure of SOTS’s method is given.A set of numerical results are demonstrated for predicting the effective parameters and the displacement and strains of composite plate.It shows that SOTS’s method can capture the 3-D local behaviors caused by3-D micro-structures well.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supported by the Special Funds for the National Basic Research Program of China (973 Project) (Grant No. 2010CB832702)the National Natural Science Foundation of China (Grant No. 90916027)also supported by NSAF (Grant No.10976004)
文摘In this paper,an atom-continuum coupled model for thermo-mechanical behaviors in micro-nano scales is presented.A representative volume element consisting of atom clusters is used to represent the microstructure of materials.The atom motions in the RVE are divided into two phases,structural deformations and thermal vibrations.For the structural deformations,nonlinear and nonlocal deformation at atomic scales is considered.The atomistic-continuum equations are constructed based on momentum and energy conservation law.The non-locality and nonlinearity of atomistic interactions are built into the thermo-mechanical constitutive equations.The coupled atomistic-continuum thermal-mechanical simulation process is also suggested in this work.
基金supported by National Natural Science Foundation of China (Grant No.90916027)Special Funds for National Basic Research Program of China (973 Program) (Grant No. 2010CB832702)the State Key Laboratory of Scientific and Engineering Computing
文摘H61der and gradient estimates for the correctors in the homogenization are presented based on the translation invariance and Li-Vogelius's gradient estimate. If the coefficients are piecewise smooth and the homogenized solution is smooth enough, the interior error of the first-order expansion is O(e) in the HSlder norm; it is O(e) in W1,∞ based on the Avellaneda-Lin's gradient estimate when the coefficients are Lipschitz continuous. These estimates can be partly extended to the nonlinear parabolic equations.
基金supported by National Natural Science Foundation of China(GrantNo.90916027)the Special Funds for National Basic Research Program of China(Grant No.2010CB832702)+1 种基金Foundation of Guizhou Science and Technology Department(Grant No.[2013]2144)the State Key Laboratory of Science and Engineering Computing
文摘This paper considers the bending behaviors of composite plate with 3-D periodic configuration.A second-order two-scale(SOTS)computational method is designed by means of construction way.First,by 3-D elastic composite plate model,the cell functions which are defined on the reference cell are constructed.Then the effective homogenization parameters of composites are calculated,and the homogenized plate problem on original domain is defined.Based on the Reissner-Mindlin deformation pattern,the homogenization solution is obtained.And then the SOTS’s approximate solution is obtained by the cell functions and the homogenization solution.Second,the approximation of the SOTS’s solution in energy norm is analyzed and the residual of SOTS’s solution for 3-D original in the pointwise sense is investigated.Finally,the procedure of SOTS’s method is given.A set of numerical results are demonstrated for predicting the effective parameters and the displacement and strains of composite plate.It shows that SOTS’s method can capture the 3-D local behaviors caused by3-D micro-structures well.
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.