In order to apply information from molecular dynamics (MD) simulations in problems governed by engineering length and time scales, a coarse graining methodology must be used. In previous work by Zhou et al (2009 Acta Mater. 57 4671-86), a traction-separation cohesive model was developed using results from MD simulations with atomistic-to-continuum measures of stress and displacement. Here, we implement this cohesive model within a combined finite element/cohesive surface element framework (referred to as a finite element approach or FEA), and examine the ability for the atomistically informed FEA to directly reproduce results from MD. We find that FEA shows close agreement of both stress and crack opening displacement profiles at the cohesive interface, although some differences do exist that can be attributed to the stochastic nature of finite temperature MD. The FEA methodology is then used to study slower loading rates that are computationally expensive for MD. We find that the crack growth process initially exhibits a rate-independent relationship between crack length and boundary displacement, followed by a rate-dependent regime where, at a given amount of boundary displacement, a lower applied strain rate produces a longer crack length. Our method is also extended to larger length scales by simulating a compact tension fracture-mechanics specimen with sub-micrometer dimensions. Such a simulation shows a computational speedup of approximately four orders of magnitude over conventional atomistic simulation, while exhibiting the expected fracture-mechanics response. Finally, differences between FEA and MD are explored with respect to ensemble and temperature effects in MD, and their impact on the cohesive model and crack growth behavior. These results enable us to make several recommendations to improve the methodology used to derive cohesive laws from MD simulations. In light of this work, which has critical implications for efforts to derive continuum laws from MD simulations, it is shown care must be taken when using a similar approach, and effects of ensemble, temperature and strain rate must be considered.
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机译：为了将分子动力学（MD）模拟中的信息应用于工程长度和时间尺度所控制的问题，必须使用粗粒度方法。在Zhou et al（2009 Acta Mater。57 4671-86）的先前工作中，使用MD模拟的结果开发了牵引分离内聚模型，并采用了从原子到连续的应力和位移度量。在这里，我们在有限元/内聚曲面元素组合框架（称为有限元方法或FEA）中实现了这种内聚模型，并检查了原子告知的FEA直接从MD复制结果的能力。我们发现，有限元分析显示了在粘结界面处应力和裂纹开口位移曲线的紧密一致性，尽管确实存在一些差异，这可以归因于有限温度MD的随机性质。然后使用FEA方法来研究较慢的加载速率，这对于MD而言在计算上是昂贵的。我们发现，裂纹扩展过程最初显示出裂纹长度和边界位移之间的速率无关关系，然后是速率依赖状态，其中在给定的边界位移量下，较低的施加应变速率会产生较长的裂纹长度。我们的方法还通过模拟具有亚微米尺寸的紧凑的拉伸断裂力学样品而扩展到更大的长度范围。这种模拟显示出比常规原子模拟大约快四个数量级的计算速度，同时展现出预期的断裂力学响应。最后，探讨了FEA和MD之间在MD的整体和温度影响以及它们对内聚模型和裂纹扩展行为的影响方面的差异。这些结果使我们能够提出一些建议，以改进从MD模拟中得出内聚规律的方法。鉴于这项工作对从MD模拟得出连续定律的努力具有关键意义，因此表明在使用类似方法时必须格外小心，并且必须考虑整体，温度和应变率的影响。
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