Effective elastic properties variability for two-layered plates of hexagonal and cubic crystals under longitudinal tension

The problem of longitudinal tension for a two-layered plate of hexagonal and cubic crystals with different orientations of crystallophysic coordinate systems is discussed. Analytical dependencies of effective Young's modulus and Poisson's ratios on thicknesses ratio are obtained. Variability of effective properties is analyzed for all possible combinations of hexagonal and cubic crystals. Significant difference between effective Young's modulus and predictions by rule of mixtures takes place in the case when one of the layers is auxetic. Effective Young's modulus can exceed Young's modulus of the stiffer layer. The ratio of Young's moduli of crystals has significant influence on effective Poisson's ratio. A FEM (finite element method) analysis of this problem was performed and its results were compared with analytical ones. Between the analytical and numerical results qualitative and quantitative correspondence takes place.

Automated summary

The issue of longitudinal tension in a two-layered plate with hexagonal and cubic crystals of different orientations is discussed, with analytical dependencies of effective properties obtained and the variability of these properties analyzed for different crystal combinations. Significant differences were found when one layer was auxetic, with the effective Young's modulus possibly exceeding that of the stiffer layer. The ratio of Young's moduli of crystals had a significant influence on the effective Poisson's ratio, with qualitative and quantitative correspondence found between analytical and numerical results.