Study of a Combined FEM-MD Method for Silicon

Abstract

A new method combining the finite element method (FEM) and the molecular dynamics (MD) for the complicated diamond-like structure of silicon is proposed. For simultaneous simulation, the patch model was used to exchange displacement information in both directions. A one-to-one correspondence of atoms and nodes is impossible for a silicon lattice, therefore, the atom was embedded in an isoparametric element. The influence of internal displacement which is a additional displacement to the continuum one, was taken into consideration. Martin’s method was applied to calculate the internal displacement and elastic constants. The conjugate gradient method was used for MD, the Newton-Raphson method was used for FEM to efficiently find the stable state, and the acceleration condition was set to raise convergence. The verification model showed that the smooth transition of displacement and stress was realized in the boundary region of FEM and MD. These values showed good agreement with the elastic solution.