Tension of thin two-layered plates of hexagonal crystals

Abstract A theoretical analysis of longitudinal stretching of a thin rectangular two-layered plate formed of hexagonal crystals with the same orientation is given. The effective elastic properties (Young’s modulus and Poisson’s ratios) of the plate are dependent on such properties of the constituent crystal as the sign and value of Poisson’s ratios, the ratio of Young’s moduli and the ratio of the thicknesses of the layers. These dependencies can be either simple or complex. It is shown that effective Young’s modulus of the two-layered plate always exceeds the result calculated by the rule of mixtures of Voigt. For small differences between Young’s moduli (or Poisson’s ratios) of the initial crystals, the accuracy of predicting effective Young’s modulus by the rule of mixtures turns out to be quite satisfactory. Effective in-plane Poisson’s ratio can be either larger or smaller than the prediction by the rule of mixtures. Special results were obtained for plates of the auxetic-nonauxetic type. In the case of plates with varying layers thickness ratios, the increase in the thickness of the auxetic layer makes it possible to control the value of negative effective in-plane Poisson’s ratio of the two-layered auxetic-nonauxetic plate.