In the context of homogenization of micro-heterogeneous materials, the choice of the $\mathcal{R}$epresentative $\mathcal{V}$olume $\mathcal{E}$lement ($\mathcal{RV\; E}$) plays a crucial role. For periodic microstructures, an $\mathcal{RV\; E}$ is an underlying unit cell with periodic boundary conditions. Nevertheless, the question of the implementation of periodic boundary conditions may arise here; for example, some of the applications of periodic boundary conditions in the literature for hexagonal cells are incorrect or they are not given in detail. In this paper, we analyze periodic boundary conditions for two-dimensional hexagonal unit cells. Periodic boundary conditions are characterized by the periodic fluctuations in the displacement fields and anti-periodic traction vectors at associated points of the boundary of the unit cell. From comparative calculations with an ensemble of unit cells, it is evident that the natural choice for vanishing fluctuations is to be set on the midpoints of the six perimeter lines of the cell. The partially applied choice of vanishing fluctuations in the six corner points of the outer edge of the unit cell leads to wrong results. The boundary conditions proposed here are analyzed on the basis of representative examples and compared to the results with the incorrect boundary conditions.

在微观异质材料均质化的背景下，$\mathcal{右}$代表性的$\mathcal{V}$奥卢梅$\mathcal{乙}$莱门特（$\mathcal{右室容积}$) 起着至关重要的作用。对于周期性微观结构，$\mathcal{右室容积}$是具有周期性边界条件的基础晶胞。然而，这里可能会出现周期性边界条件的实施问题；例如，文献中对于六边形单元的周期性边界条件的一些应用是不正确的或者没有详细给出。在本文中，我们分析了二维六边形晶胞的周期性边界条件。周期性边界条件的特征是晶胞边界相关点处的位移场和反周期牵引矢量的周期性波动。通过与晶胞集合的比较计算，很明显，消失波动的自然选择是设置在晶胞的六条周长线的中点。部分应用晶胞外边缘六个角点波动消失的选择会导致错误的结果。这里提出的边界条件是在代表性例子的基础上进行分析的，并与不正确边界条件的结果进行比较。