Development and Implementation of Recursive Coarse-Grained Particle Method for Meso-Scale Simulation

Abstract

A coarse-graining method has been proposed [R. E. Rudd and J. Q. Broughton: Phys. Rev. B 58 (1998) R5893–R5896] for a crystalline system of atoms, in which the inter-particle interaction is obtained through coarse-graining of the partition function of the atomic Hamiltonian in the harmonic approximation. Though the method has attractive features such as its natural incorporation of atomistic phonons, the original formulation limits its application to small periodic systems without surfaces. In this paper, we improve the method as follows: (i) we introduce a recursive coarse-graining procedure to overcome the size limitation problem, (ii) we rewrite the deformation energy in both translation and rotation invariant form to make it applicable to macroscopically deformed systems, (iii) we extend the formulation for multi-component systems, and (iv) we incorporate the thermal expansion and softening of the atomistic systems. The essentials in the code implementation are explained. The method is successfully applied to deforming nanorods of sub-micron size in both two and three dimensions, to show that it is ready for dynamics simulation of meso-scale, three-dimensional realistic systems.