论文标题
脆性纳米线的连续模型，该模型从原子描述中得出$γ$ -Convergence
A continuum model for brittle nanowires derived from an atomistic description by $Γ$-convergence
论文作者
论文摘要
从具有短距离相互作用的粒子系统开始，我们得出了一个连续模型，用于在三维空间中移动的不可扩展杆的弯曲，扭转和脆性断裂。由于颗粒的数量倾向于无穷大，因此假定杆的厚度与原子间距离相同。 $γ$ - 限制中的断裂能由隐式细胞配方表示，该公式涵盖了不同的裂缝模式，包括（完整的）裂纹，褶皱和扭转裂纹。在特殊情况下，可以显着简化细胞公式。我们的方法适用于例如具有Lennard-Jones型潜力的原子系统，并由陶瓷纳米线的研究激发。
Starting from a particle system with short-range interactions, we derive a continuum model for the bending, torsion, and brittle fracture of inextensible rods moving in three-dimensional space. As the number of particles tends to infinity, it is assumed that the rod's thickness is of the same order as the interatomic distance. Fracture energy in the $Γ$-limit is expressed by an implicit cell formula, which covers different modes of fracture, including (complete) cracks, folds and torsional cracks. In special cases, the cell formula can be significantly simplified. Our approach applies e.g. to atomistic systems with Lennard-Jones-type potentials and is motivated by the research of ceramic nanowires.
