Open Access

ARTICLE

An Atom-Based Continuum Method for Multi-element Crystals at Nano Scale

Xianqiao Wang¹, James D. Lee²

1 Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052 xqwang@gwmail.gwu.edu.
2 Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052 jdlee@gwu.edu

Computer Modeling in Engineering & Sciences 2010, 69(3), 199-222. https://doi.org/10.3970/cmes.2010.069.199

Abstract

This paper presents an atom-based continuum (ABC) method aiming at a seamless transition from the atomistic to the continuum description of multi-element crystalline solids (which has more than one kind of atom in the unit cell). Contrary to many concurrent multiscale approaches, ABC method is naturally suitable for the analysis of multi-element crystals within a finite element (FE) framework. Taking both efficiency and accuracy into account, we adopt a cluster-based summation rule for atomic force calculations in the FE formulations. Single-crystals MgO, BaTiO₃ and Cu under mechanical loading are modeled and simulated. With a coarse-grained mesh, ABC method is shown to be able to simulate dynamic and nonlinear behaviors, such as wave propagation and polarization, of multi-element crystalline materials. It is demonstrated that by reducing the finite element mesh to the atomic scale, in other words, let the finite element size equal to the size of a unit cell, critical phenomena at atomic scale such as crack propagation can be successfully reproduced.

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