石墨烯的Föppl-vonKármán原子模型
An atomistic-based Föppl-von Kármán model for graphene
摘要：
我们推导出一个非线性连续模型的情况下，有限的面外位移和小的面内变形的石墨烯。在假设晶格相互作用由Brenner的REBO势的第二代和自应力是存在的，我们引入离散应变措施占到第三邻居的相互作用。的连续极限原来取决于一个平均（宏观）位移场和相对位移的两个布拉维晶格，引起的六边形周期性。在最小化关于位移变量的能量的基础上，我们正式确定了一个Föppl-vonKármá型的连续介质模型，其本构系数由原子间相互作用给出。
英文摘要：
We deduce a non-linear continuum model of graphene for the case of finite out-of-plane displacements and small in-plane deformations. On assuming that the lattice interactions are governed by the Brenner's REBO potential of 2nd generation and that self-stress is present, we introduce discrete strain measures accounting for up-to-the-third neighbor interactions. The continuum limit turns out to depend on an average (macroscopic) displacement field and a relative shift displacement of the two Bravais lattices that give rise to the hexagonal periodicity. On minimizing the energy with respect to the shift variable, we formally determine a continuum model of Föppl-von Kármá type, whose constitutive coefficients are given in terms of the atomistic interactions.
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