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力学学报  2015 

类石墨烯二维原子晶体的微态理论模型

DOI: 10.6052/0459-1879-14-282, PP. 451-457

Keywords: 二维原子晶体,微态理论,材料常数,声子色散关系,本构方程

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Abstract:

基于微态(Micromorphic)连续介质理论,提出了针对类石墨烯二维原子晶体的新力学模型.该模型以有限大小的布拉维单胞为基元体,考虑基元粒子的宏观位移和微观变形,依据微态理论基本方程,推导了全局坐标系下模型的主导方程.然后针对布拉维单胞中含有两个原子的类石墨烯晶体,通过分析单胞中声子振动模式与基元体自由度的关系,获得了微态形式下声子色散关系的久期方程,并根据二维晶体声子色散特性对久期方程进行了简化,进而确定了类石墨烯晶体模型的本构方程.最后,以石墨烯和单层六方氮化硼为例,利用简化的表达式拟合了它们面内声子色散关系数据,计算了模型材料的常数,石墨烯模型的等效杨氏模量、泊松比分别为1.05TPa和0.197,氮化硼分别为0.766TPa和0.225,均与已有的实验值相符合.

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