Nano-Micro Scale Transition via Atomistic-Continuum Coupling by Homogenization

基于经典原子间势的分子计算机模拟能够以高的时间和空间分辨率描述材料的性质和过程。然而，它们被限制在较小的系统尺寸(通常为10亿个原子)。因此，宏观长度尺度是遥不可及的。本研究项目的目标是开发一种双尺度原子-连续介质耦合方法，通过均化来实现纳米非均质固体的纳米-微观转变。因此，基于原子间相互作用势的材料和结构行为的模拟将被推进到迄今为止无与伦比的长度尺度。所提出的原子-连续耦合方法将通过验证和测试的并行模拟工具的有效组合来实现。为了实现这一目标，该研究项目建立在现有的理论和方法概念的FE$^2$方法和FE-HMM的基础上，它们本身是基于称为Hill-Mandel条件的两个长度尺度的能量密度的等价性。与FE和FE-HMM框架中的微观-宏观转变不同，预期的纳米-微观尺度转变不能依赖于代表性体积元素水平上的连续本构关系。为此，选择使用分析的原子间相互作用势。在纳米尺度上使用分子静力学解算器，该解算器通过接口连接到微型有限元解算器。界面上的耦合量是从微观到宏观的微观变形梯度，从纳米到微观的第一Piola-Kirchhoff应力张量，以及有效切线模数。对于选定的材料系统，应评估其精度、稳定性和收敛特性，以及在弹性到大弹塑性变形范围内的性能。在感兴趣的材料体系中，特别是纳米多晶、具有空间分布位错的单晶和纳米孔结构。利用这种双尺度耦合方法，通过均匀化，将基于原子间相互作用势精度的材料和结构性质的模拟提升到了迄今为止被认为是无法达到的长度尺度。

Molecular computer simulations based on classical interatomic potentials enable the description of material properties and processes in high temporal and spatial resolution. They are, however, confined to small system sizes (typically < 1 billion atoms). Consequently, macroscopic length scales are out of reach. The goal of this research project is the development of a two-scale atomistic-continuum coupling method which realizes through homogenization a nano-micro transition for nanoheterogeneous solids. Thereby the simulation of material and structural behavior based on interatomic potentials shall be advanced to so far unmatched length scales.The proposed atomistic-continuum coupling method shall be realized by an effective combination of proof and tested, parallelized simulation tools. To reach that target the research project builds on existing theoretical and methodological concepts of the FE$^2$-method and the FE-HMM, which themselves are based on the equivalence of energy densities of both length scales referred to as Hill-Mandel condition. In contrast to micro-macro transitions in the framework of FE$^2$ and FE-HMM, the intended nano-micro scale transition can not rely on a continuum constitutive law on the level of representative volume elements. For that reason the use of analytical interatomic potentials is chosen. A molecular statics solver is used on the nanoscale, which is connected through an interface to the micro-FEM solver. The coupling quantities at the interface are, from micro to macro the microscopic deformation gradient, from nano to micro the first Piola-Kirchhoff stress tensor obtained from averaging over the representative volume element, as well as the effective tangent moduli. Accuracy, stability and convergence properties as well as the performance of this hybrid method shall be assessed for selected materials systems in the broad range of elastic up to large elastic-plastic deformations. Among the materials systems of interest there are in particular nanocrystalline polycrystals, single crystals having spatially distributed dislocations, and nanoporous structures. By means of this two-scale coupling method through homogenization the simulation of material and structural properties based on the accuracy of interatomic potentials is lifted to length scales that were seen as inaccessible till now.