On molecular statics and surface-enhanced continuum modeling of nano-structures
On molecular statics and surface-enhanced continuum modeling of nano-structures
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DOI：
10.1016/j.commatsci.2012.11.053
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发表时间：
2013-03
影响因子：
3.3
通讯作者：
D. Davydov;A. Javili;P. Steinmann
中科院分区：
文献类型：
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作者：
D. Davydov;A. Javili;P. Steinmann
几十年来，科学界一直在讨论离散公式和连续公式之间可能存在的联系。对连续介质场（主要是应力）提出了不同的原子表达式。例如，可以将离散模型与基于欧拉结构中的空间平均的连续体公式联系起来，然后进行概率（统计）平均。作为欧拉平均法的一种替代方法，拉格朗日平均法最近被提出。这两种方法都允许从原子模拟中计算局部连续体场。从连续体公式的角度来看，固体在纳米尺度上的行为可以基于表面增强连续体（SEC）理论来捕获，即表面具有自己的本构结构。连续体模型相对于原子模型的一个明显优势是提高了计算效率。在这篇文章中，我们比较了从分子静力学（MS）模拟中获得的原子场与从SEC理论的数值近似中获得的原子场。连续本构模型的体弹性参数直接由原子模型得到。以面心立方（FCC）铜为例，对两种方法进行了比较。正如在原子模拟中观察到的那样，连续统公式在表面能的作用下增强了模型尺寸效应的能力。用连续和离散两种方法求得的局部场是一致的。研究了从原子到连续体过程得到的结果与平均半径和自由表面接近度的关系。欧拉平均法和拉格朗日平均法对这里考虑的FCC晶体给出了可比较的结果。
Possible links between discrete and continuum formulations have been discussed in the scientific community since several decades. Different atomistic expressions for the continuum fields (most importantly stresses) were proposed. As an example, it is possible to link discrete models to a continuum formulation based on spatial averaging in the Eulerian configuration followed by probability (statistical) averaging. As an alternative to Eulerian averaging, Lagrangian averaging has been recently proposed. Both approaches allow calculation of the local continuum fields from atomistic simulations. From the continuum formulation perspective, the behavior of solids at the nanoscale can be captured based on a surface-enhanced continuum (SEC) theory whereby the surface is equipped with its own constitutive structure. A distinct advantage of continuum models over their atomistic counterparts is the increased computational efficiency. In this contribution we compare atomistic fields obtained from molecular statics (MS) simulations to their counterpart, obtained from numerical approximations to the SEC theory. Bulk elastic parameters for the continuum constitutive model are obtained directly from the atomistic model. A representative numerical simulation of face-centered-cubic (FCC) copper is used to compare the two approaches. The ability of the continuum formulation enhanced with a surface energy to model size effects, as observed in the atomistic simulations, is shown. The local fields evaluated using both the continuum and discrete approach are in a good agreement. The dependence of the results obtained from the atomistic-to-continuum procedure on both the averaging radius and the proximity of the free surface is studied. Eulerian and Lagrangian averaging approaches are shown to give comparable results for the here considered FCC crystal.