Mechanical Behavior of Atoms Using Atomic-scale Finite Element Method
Daniela Andrade Damasceno Damasceno1; Nimal Rajapakse Rajapakse2; Euclides Mesquita Mesquita1
1 Faculty of Mechanical Engineering, Unicamp, Campinas, SP; 2 School of Engineering Science, Simon Fraser University, Burnaby, BC
doi:10.20906/CPS/CILAMCE2015-0892
Resumo
This paper presents a formulation of the Atomic-scale Finite Element Method (AFEM) [Liu et al. 2004] for one and two dimensional analysis of the mechanical behavior of set of atoms. In the present implementation Leonard-Jones potential is used to describe the interaction between atoms. AFEM uses both first and second derivatives from a molecular force field to derive, respectively, the system matrix and the load vector. A series of topics are investigated within this article, including the cut off radius of the interatomic potential, the notion of an atomistic finite element and a scheme for imposing boundary conditions at the atoms level which takes into account non-local effects. Force-strain relations are obtained numerically. The numerical results obtained from procedure envisaged in this work are compared to a standard Molecular Dynamics implementation running on the LAMMPS software. Accuracy and numerical efficiency of the AFEM compared to MD is addressed. B.Liu, Y. Huang, H. Jiang, S. Qu and K.C. Hwang, The atomic-scale finite element method, Comput. Methods Appl. Mech. Engrg, Vol. 193, 1849- 1864 (2004).
Palavras-chave: AFEM; MD; Lennard Jones