Damage of materials inherently involves coupling of deformation and failure mechanisms at multiple length and time scales. This paper develops self-consistent elastic constitutive relations of crystalline materials containing atomistic scale cracks, from observations made in a concurrent multi-scale simulation system coupling atomistic and continuum domain models. The self-consistent constitutive model incorporates both nonlinearity and nonlocality to account for atomic level interactions and deformation mechanisms, especially near crack tips. Atomistic modeling in the concurrent model is done using molecular dynamics (MD), while the continuum modeling is done using a crystal elasticity finite element (FE) analysis code. The atomistic–continuum coupling is achieved by enforcing geometric compatibility and force equilibrium in an interface region. The constitutive model is calibrated by comparing with the results of MD predictions in the concurrent model. For validation, the crack tip stress field is investigated using both the coupled concurrent model and a FE model with the constitutive law. The self-consistent model exhibits excellent accuracy and enhanced efficiency in comparison with pure MD and concurrent model results.

中文翻译：

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用于开发具有裂纹的晶体的自洽弹性本构模型的并发原子连续模型

材料的损坏本质上涉及在多个长度和时间尺度上耦合变形和失效机制。本文根据在耦合原子域和连续域模型的并发多尺度模拟系统中进行的观察，开发了包含原子尺度裂纹的晶体材料的自洽弹性本构关系。自洽本构模型结合了非线性和非局域性来解释原子级相互作用和变形机制，尤其是在裂纹尖端附近。并发模型中的原子建模是使用分子动力学 (MD) 完成的，而连续模型是使用晶体弹性有限元 (FE) 分析代码完成的。原子-连续耦合是通过在界面区域强制几何兼容性和力平衡来实现的。本构模型是通过与并发模型中的 MD 预测结果进行比较来校准的。为了验证，裂纹尖端应力场使用耦合并发模型和具有本构定律的有限元模型进行研究。与纯 MD 和并发模型结果相比，自洽模型具有出色的准确性和更高的效率。