类石墨烯二维原子晶体的微态理论模型

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1.05 TPa 和0.197,氮化硼分别为0.766 TPa 和0.225,均与已有的实验值相符合. 

MICROMORPHIC MODEL OF GRAPHENE-LIKE TWO-DIMENSIONAL ATOMIC CRYSTALS

A novel mechanical model is proposed for graphene-like two-dimensional (2D) atomic crystals based on micromorphic continuum theory, in which the macro-displacement and micro-deformation of a basal element in the Bravais cell of finite size are considered. The governing equations of the model are derived from the basic equations of micromorphic theory in global coordinates. For the Bravais cell of graphene-like crystals containing two atoms, the secular equations of phonon dispersions are then obtained in micromorphic form by analyzing the relations between the vibrational modes of phonons and the independent degrees of freedom of the basal elements, and are further simplified according to the properties of phonon dispersion of 2D crystals, thus the constitutive equations of the model are conformed. Finally, the material constants are determined respectively by fitting the data of the in-plane phonon dispersion relations of graphene and monolayer hexagonal boron nitride with the simplified expressions. The obtained equivalent Young's modulus and Possion' ratio of graphene are 1.05 TPa and 0.197 respectively, and those of monolayer hexagonal boron nitride are 0.766 TPa and 0.225 respectively; both show good agreements with available experimental values.