Two‐Layered Tubes from Cubic Crystals: Auxetic Tubes

Abstract

Effective Young's modulus and Poisson's ratios of two‐layered cylindrical hollow tubes made of cubic crystals (auxetics and nonauxetics) are considered. An analysis of longitudinal tension of stretching tubes is performed within the framework of curvilinear‐anisotropic elasticity and Saint‐Venant's approximation. Analytical dependences of effective Young's modulus on the compliance coefficients of the initial crystals and layer thickness as ratio of composites auxetics–nonauxetics are obtained. Deviations from the “rule of mixtures” predictions which increase with increasing Young's modulus of initial nonauxetics are demonstrated. It is found that effective Poisson's ratios of two‐layered tubes depend on the ratio of their thicknesses, the dimensionless combinations of compliance coefficients and a dimensionless radial distance. An effect of tube components on negativeness of effective Poisson's ratio of the composite auxetics–nonauxetics proved to be strongly dependent on the value of Young's modulus for nonauxetic component. It is shown that effective Poisson's ratios for some characteristics of the initial crystals and ratios of layer thicknesses may fall outside the limits on Poisson's ratios of isotropic materials. It is shown that many two‐layered tubes composed of pairs of nonauxetics can have large negative effective Poisson's ratios.