连续介质理论在研究碳纳米管力学性能中的应用进展

综述连续介质理论在微尺度力学，尤其是在碳纳米管力学性质研究中的应用及进展。介绍近期发展的用于模拟碳纳米管力学行为的各种连续介质模型的理论框架与典型算例。重点阐明各连续介质模型实现宏微观关联的基本思想，详述碳纳米管的桁架模型、Yakobson和Ru等人的壳模型(shell model)、Arroyo和Belytschko的薄膜模型(membrane model)以及Tadmor、Ortiz和Phillips的准连续介质理论；归纳、总结这些理论模型的基本假设、主要结论及其局限性；分析指出它们所涉及的理论推导与数值算法中的一些关键因素；简要介绍这些理论在微尺度力学中的应用。最后，预测连续介质理论应用于微尺度现象分析的发展趋势，指出今后的研究方向。

ADVANCE IN THE APPLICATION OF CONTINUUM THEORY TO INVESTIGATE THE MECHANICAL PROPERTIES OF CARBON NANOTUBES

Application of continuum theory to micro scale mechanics, especially to investigation of mechanical properties of carbon nanotubes is summarized. The theoretical framework and some typical examples of various recently developed continuum models used in modeling mechanical behaviors of Carbon nanotubes are introduced. The focus is on the ideas how to realize the macro micro correspondence in the continuum models. Some typical models, such as truss model, shell model by Yakobson and Ru, membrane model by Arroyo and Belytschko. And quasi continuum theory by Tadmor, Ortiz and Phillips, are discussed in detail. The fundamental assumptions, main conclusions and limitations of these models are concluded. The key factors of the theoretical analysis and numerical algorithm concerned with them are pointed out. The applications of these continuum models to the micro scale mechanics are also introduced briefly. Finally, the trends and directions on using continuum theory to research micro scale phenomena are predicted.