摘要
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.
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.
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)
