Longitudinal elastic tension of two-layered plates from isotropic auxetics-nonauxetics and cubic crystals

Elastic longitudinal tension of thin two-layered plate composed of materials having positive and negative Poisson's ratios (auxetics and nonauxetics) is considered. Isotropic materials and crystals with cubic fourfold symmetry axis coinciding with the direction of tension are analyzed. The analytical dependences for effective Poisson's ratios of the plates on the ratio of layer thicknesses, Poisson's ratios and Young's moduli ratios of initial joined materials are derived. It was found that effective Poisson's ratio do not follow the rule of mixtures. Violation is particularly essential for the strong initial isotropic auxetics and incompressible isotropic nonauxetics. Derivation of general formulas for effective Poisson's ratios and effective Young's modulus of two-layered plates from cubic crystals is given. The derived formula for effective Young's modulus in the limit of initial isotropic materials coincides with formulas obtained previously in the literature. We show several examples of cubic crystals, auxetics-nonauxetics such that effective Poisson's ratios of two-layered plates may substantially exceed Poisson's ratios of the initial crystals. Effective Young's modulus may also exceed Young's moduli of both initial crystals.