Abstract

In the framework of the theory of anisotropic elasticity, a theoretical analysis of the out-of-plane extension of thin two-layered plates of hexagonal crystals is carried out. The six-fold axes of all pairs of crystals are assumed to be perpendicular to the plane of the plates. Formulae for effective Young’s modulus and effective Poisson’s ratio are obtained. It is shown that in most cases effective Young’s moduli exceed Reuss’s average, and thus the rule of mixtures is violated. Equality of these characteristics is possible if the ratios of Young’s moduli and the ratios of Poisson’s ratios of crystal pairs are the same. Effective Poisson’s ratio may be greater or less than the corresponding Reuss’s average. In addition, it was found that effective Young’s modulus can surpass Young’s moduli of both crystals forming a two-layered plate. Effective Poisson’s ratio can be both larger and smaller than Poisson’s ratios of the initial pair of crystals. The general theoretical conclusions are illustrated by numerical estimates using the experimental values of the elastic constants of the known hexagonal crystals.

中文翻译：

---

同向六方晶两层薄板的面外张力

摘要

在各向异性弹性理论的框架内，对六方晶薄两层板的面外延伸进行了理论分析。假定所有晶体对的六重轴都垂直于板平面。获得了有效杨氏模量和有效泊松比的公式。结果表明，在大多数情况下，有效杨氏模量超过了 Reuss 的平均值，因此违反了混合规则。如果晶体对的杨氏模量比和泊松比比相同，则这些特性的相等是可能的。有效泊松比可能大于或小于相应的 Reuss 平均值。此外，发现有效杨氏模量可以超过形成双层板的两种晶体的杨氏模量。有效泊松比可以大于或小于初始晶体对的泊松比。一般的理论结论通过使用已知六方晶体的弹性常数的实验值的数值估计来说明。