Meshless Dynamic Relaxation Techniques for Simulation Atomic Structures of Materials

Abstract

<p> 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. This thesis introduces a 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.</p> <p> 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 choice of scaled mass of atoms, proper time step, boundary conditions and damping appropriate for the efficient and stable simulation is studied.</p> <p> A small block of atoms is used to obtain the numerical responses from a hybrid algorithm of potential energy functions and Dynamic Relaxation techniques such as repulsion and attraction in pair potential, minimum configuration, damping effects and different boundary conditions.</p> <p> The simulation using modified Dynamic Relaxation techniques is performed to the real material model with dislocation defect. The results after relaxation are in agreement with the prediction and current Molecular Dynamics simulation. Therefore, Dynamic Relaxation could be an alternative tool for atomistic simulation.</p>