Coarse-grained Molecular Dynamics Models for Crystalline Solids at Finite Temperature

原子模型，如分子动力学，在许多应用中是非常有用的计算工具，特别是在原子尺度结构对整体性质至关重要的情况下。一个完整的原子模型通常是计算上难以处理的，因为它有大量的自由度。 该项目的主要目标是开发粗粒度模型，以便能够以更低的成本进行计算机模拟。而不是依赖于经验的本构关系，这项工作的目的是推导出粗尺度模型直接基于分子动力学使用投影形式主义。作为一个应用，粗粒模型将被应用于位错动力学，研究固体系统与位错的混合物的响应。在原子尺度上，晶体固体包含许多精细结构的缺陷，并且详细的配置，例如缺陷的类型，取向和浓度，最终负责材料在宏观尺度上的机械性能。 原子模型，如分子动力学，直接考虑组成原子的相互作用。 然而，主要的挑战是，这样的系统通常太大，不适合任何实际计算。此外，还不清楚感兴趣的宏观量与原子位置的关系。这项工作提供了一个系统的方法来减少原子模型的大小，而不影响精度。简化模型将使模拟真实尺寸的系统成为可能，并为许多材料过程的微观机制提供有价值的见解。

Atomistic models, such as molecular dynamics, have been very useful computational tools in many applications, especially where atomic-scale structures are crucial to the overall properties. A full atomistic model is often computationally intractable due to the huge number of degrees of freedom. The main objective of this project is to develop coarse-grained models so that computer simulations can be conducted at a much reduced cost. Rather than relying on empirical constitutive laws, this work aims to derive the coarse-scale model directly based on molecular dynamics using a projection formalism. As an application, the coarse-grained models will be applied to dislocation dynamics, to study the response of a solid system with a mixture of dislocations.At the atomic scale, crystalline solids contain many defects of delicate structures, and the detailed configurations, e.g. the type of defects, orientations, and concentrations, are ultimately responsible for the mechanical properties of the material at the macroscopic scale. Atomistic models, such as molecular dynamics, directly take into account the interaction of the constituting atoms. The main challenge, however, is that such a system is usually too large to fit in any practical computation. In addition, it is not clear how macroscopic quantities of interest are related to the position of the atoms. This work offers a systematic approach to reduce the size of atomistic models, without compromising the accuracy. The reduced model will make it possible to simulate systems of realistic size, and provide valuable insight on the microscopic mechanism underlying many material processes.