arXiv 1801.050502018-01-15cond-mat.mtrl-sci

一些2D晶体的本构建模：石墨烯、六方BN、MoS $_2$、WSe $_2$和NbSe $_2$

Constitutive modeling of some 2D crystals: graphene, hexagonal BN, MoS$_2$, WSe$_2$ and NbSe$_2$

D. Sfyris, G. I. Sfyris, C. Galiotis

备注：: 3 figures
发表信息：: To access the final edited and published work see International Journal of Solids and Structures Volume 66, 1 August 2015, Pages 98-110
DOI：: 10.1016/j.ijsolstr.2015.03.030

摘要：

我们制定了一个非线性弹性本构框架的建模一些目前感兴趣的二维晶体。我们处理的2D晶体是石墨烯、六方氮化硼和一些金属二硫属化物：二硫化铼（MoS $_2$）、钨硒（WSe $_2$）和二硒化铌（NbSe $_2$）。我们首先利用单原子和双原子2-网理论找到它们的算术对称性。然后，通过限制到弱变换邻域和应用柯西-玻恩规则，我们能够使用连续介质力学利用的对称性：几何对称性。我们给出了依赖于平面内测度、曲率张量和位移向量的能量的完全不可约表示。这是对描述对称性如何在连续统水平上变化的对称性层次结构进行的：$\mathcal C_{6 ν} \rightarrow \mathcal C_{2 ν} \rightarrow \mathcal C_1$用于单原子2-网，$\mathcal C_{6 ν} \rightarrow \mathcal C_{1 ν} \rightarrow \mathcal C_1$用于双原子2-网。有了这些能量，我们就能够计算出每个对称区域的应力和偶应力。

英文摘要：

We lay down a nonlinear elastic constitutive framework for the modeling of some 2D crystals of current interest. The 2D crystals we treat are graphene, hexagonal boron nitride and some metal dichalcogenides: molybdenium disulfide (MoS$_2$), tungsten selenium (WSe$_2$), and niobium diselenide (NbSe$_2$). We first find their arithmetic symmetries by using the theory of monoatomic and diatomic 2-nets. Then, by confinement to weak transformation neighbourhoods and by applying the Cauchy-Born rule we are able to use the symmetries continuum mechanics utilizes: geometric symmetries. We give the complete and irreducible representation for energies depending on an in-plane measure, the curvature tensor and the shift vector. This is done for the symmetry hierarchies that describe how symmetry changes at the continuum level: $\mathcal C_{6 ν} \rightarrow \mathcal C_{2 ν} \rightarrow \mathcal C_1$ for monoatomic 2-nets and $\mathcal C_{6 ν} \rightarrow \mathcal C_{1 ν} \rightarrow \mathcal C_1$ for diatomic two nets. Having these energies at hand we are able to evaluate stresses and couple stresses for each symmetry regime.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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