英文版纳米尺度固体中有限元法的应用研究.doc

Research on the application about finite element method at nano-scale metal crystal Abstract: The paper carefully analysis the law of atomic motion at nano-scale metal crystal, giving the equilibrium equation. A multi-scale calculation method on simulating the mechanical behavior of metal crystal is present at nano-scale. Engineering stress is used to calculate the distribution law of the stress in internal crystal metal and a theory is generated about the finite element applying in nano-scale. The tensile of single crystal nano-copper rods which have defect and no defect were simulated using finite element method and molecular dynamics. The results proved that finite element method could be used in nano-scale metal crystal. Keywords: multi-scale method, stress, order, metal crystal 1. Introduction In recent years advanced materials have been developed that have the potential to revolutionize structural design and which require the development of new methods in applied mechanicsl. This revolution has been inhibited by a lack of understanding of both the fundamental behavior of these material at multiple scales (in particular the sub-micron or nano-scale), and the links between these scales. Molecular dynamics (MD) method widely applied in nanoscale is a classics numerical method. Spatial scale of calculation always stays in nanometer level and time scale also keep in femto-second level. MD method as a discrete numerical method takes the atoms as partials, the force from one atom to another is determined by potential function and the displacement, velocity, and acceleration of each atom is calculated by Newton law. The advantages of MD method could simulate kinds of models and give the microscopic characteristic of materials. With the expanding of simulation scale, the amount of calculation increased on geometric series, the scale could be analyzed is limited greatly. Size effect on deformation twinning was analyzed (Qian Yu [1]) in the model which reached hundreds