单层石墨烯力学性能尺寸效应的有限元分析

本文采用杆件系统模拟单层石墨烯结构，其中石墨烯的碳-碳共价键视为杆件，碳原子视为杆件之间的连接点。基于杆件系统的有限元方法，计算出单层石墨烯的杨氏模量、剪切模量和泊松比等力学性能参数。在此基础上，构建尺寸从小到大的8个单层石墨烯计算模型，求得各种尺寸下杨氏模量、剪切模量和泊松比等力学性能参数。通过分析这些力学性能参数随着尺寸变化而变化的结果，研究单层石墨烯力学性能的尺寸效应。数值算例表明，在小尺寸下扶手型和锯齿型单层石墨烯力学性能的尺寸效应显著，而随着计算模型尺寸的增大，尺寸效应出现弱化；并且相同尺寸的情况下，扶手型单层石墨烯的杨氏模量和剪切模量总是大于锯齿型的相应量。

Finite Element Analysis of Size Effect on Mechanical Properties of Monolayer Graphene

A frame system was used to simulate the monolayer graphene structure, in which the carbon-carbon covalent bond was considered as the beam and the carbon was considered as the node. Based on the finite element method of the frame system, the parameters of mechanical properties such as Young''s modulus, shear modulus and Poisson''s ratio of the monolayer graphene can be computed. On this foundation, eight computational models with different size were constructed for those parameters of mechanical properties of the monolayer graphene. Size effect on the mechanical properties was investigated by the analysis of the mechanical property changes with different size. Numerical examples show that the size effect on the mechanical properties of armchair and zigzag monolayer graphene is obvious under the small size. However, the size effect is weakened as the size of the computational model increases. Young''s modulus and shear modulus of armchair monolayer graphene are larger than the corresponding ones of zigzag monolayer graphene.