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arXiv 1503.03944cond-mat.mtrl-sci
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一个综合的石墨烯晶格稳定性极限面

A comprehensive lattice-stability limit surface for graphene

Sandeep Kumar, David Parks

摘要:

使用晶格动力学稳定性分析,在各种负载下的石墨烯的可逆变形的限制进行检查。然后,这些信息被用来构建一个全面的晶格稳定性极限表面的石墨烯,它提供了一个分析描述的初期晶格不稳定性的\textit{all kinds},任意变形,参数化的应变/应力的不变量。对称不变量允许以最少数量的系数获得精确的参数化。基于这个极限面,我们推导出了一个石墨烯晶格稳定性的一般连续判据:当偏应变$γ$的大小达到一个临界值$γ^c$时,出现不稳定性,该临界值依赖于平均静应变$\bar {\mathcal E}$和偏拉伸的方向性$θ$.我们还区分了极限表面的不同区域,这些区域对应于石墨烯中晶格不稳定性的根本不同机制,例如结构与材料不稳定性,以及长波(弹性)与短波不稳定性。通过在连续有限元分析(FEA)中实施,在无缺陷石墨烯的初期失效评估中证明了该极限表面的实用性。由此产生的方案不仅能够实时评估宏观条件(例如,载荷;挠度)以及微观条件(例如,局部应力/应变;空间位置、时间接近度和初始晶格不稳定性的性质),在所述初始晶格不稳定性处,不稳定性发生在经受任意负载条件的无缺陷石墨烯片中。

英文摘要:

The limits of reversible deformation in graphene under various loadings are examined using lattice-dynamical stability analysis. This information is then used to construct a comprehensive lattice-stability limit surface for graphene, which provides an analytical description of incipient lattice instabilities of \textit{all kinds}, for arbitrary deformations, parametrized in terms of symmetry-invariants of strain/stress. Symmetry-invariants allow obtaining an accurate parametrization with a minimal number of coefficients. Based on this limit surface, we deduce a general continuum criterion for the onset of all kinds of lattice-stabilities in graphene: an instability appears when the magnitude of the deviatoric strain $γ$ reaches a critical value $γ^c$ which depends upon the mean hydrostatic strain $\bar {\mathcal E}$ and the directionality $θ$ of the deviatoric stretch. We also distinguish between the distinct regions of the limit surface that correspond to fundamentally-different mechanisms of lattice instabilities in graphene, such as structural vs material instabilities, and long-wave (elastic) vs short-wave instabilities. Utility of this limit surface is demonstrated in assessment of incipient failures in defect-free graphene via its implementation in a continuum Finite Elements Analysis (FEA). The resulting scheme enables on-the-fly assessments of not only the macroscopic conditions (e.g., load; deflection) but also the microscopic conditions (e.g., local stress/strain; spatial location, temporal proximity, and nature of incipient lattice instability) at which an instability occurs in a defect-free graphene sheet subjected to an arbitrary loading condition.

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