论文标题
薄和超薄杆作为$γ$的原子模型限制的弯曲扭转理论
A bending-torsion theory for thin and ultrathin rods as a $Γ$-limit of atomistic models
论文作者
论文摘要
本说明的目的是建立两种连续理论，用于将不可扩展的杆弯曲和扭转为3D原子模型的$γ$限制。在我们的派生中，我们研究了消失的杆厚度$ h $和原子间距离$ \ varepsilon $的同时限制。首先，我们为由有限的许多原子纤维（$ \ varepsilon \ sim h $）组成的超薄杆建立了一种新颖的理论，该杆将表面能和新的离散术语包含在限制功能中。可以将其视为对纳米线的机械建模的贡献。其次，我们将$ \ varepsilon \ ll h $的情况处理并恢复非线性杆型$ - $ $ $的现代版本的Kirchhoff Rod理论。
The purpose of this note is to establish two continuum theories for the bending and torsion of inextensible rods as $Γ$-limits of 3D atomistic models. In our derivation we study simultaneous limits of vanishing rod thickness $h$ and interatomic distance $\varepsilon$. First, we set up a novel theory for ultrathin rods composed of finitely many atomic fibres ($\varepsilon\sim h$), which incorporates surface energy and new discrete terms in the limiting functional. This can be thought of as a contribution to the mechanical modelling of nanowires. Second, we treat the case where $\varepsilon\ll h$ and recover a nonlinear rod model $-$ the modern version of Kirchhoff's rod theory.
