The Meshless Dynamic Relaxation Techniques for Simulating Atomic Structures of Materials

Traditionally, Molecular Dynamics combined with pair potential functions or the Embedded Atom Method (EAM) is applied to simulate the motion of atoms. When a defect is generated in the crystalline lattice, the equilibrium of atoms around it is destroyed. The atoms move to find a new place where the potential energy in the system is minimum, which could result in a change of the local atomic structure. The present paper introduces new Dynamic Relaxation algorithm, which is based on explicit Finite Element Analysis, and pair or EAM potential function, to find equilibrium positions of the block of atoms containing different structural defects. The internal force and stiffness at the atoms (nodes) are obtained by the first and second derivatives of the potential energy functions. The convergence criterion is based on the Euclidean norm of internal force being close to zero when the potential energy is minimum. The damping ratio affects the solution path so that different damping ratios could lead to different minimum potential energy and equilibrium shapes. The numerical responses and results by applying free boundary conditions and certain periodic boundary conditions are presented. The choice of scaled mass of atoms, proper time step and damping appropriate for the efficient and stable simulation is studied.