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Spherical Auxetic Shells

Materials that exhibit negative Poissons ratio are called auxetic materials. Although such materials are quite rare, they nevertheless exist as naturally occurring materials and artificially made materials. Due to their unique material properties, auxetic materials have been intensively investigated for the past 20 years. This paper studies the effect of auxeticity on the maximum stresses in spherical shells. The results suggest that auxetic materials are not suitable for shells with built-in edge, but highly suitable for shells that are simply supported. For the latter boundary condition, it was found that the ratio of maximum bending stress to the maximum membrane stress diminishes as the Poissons ratio of the shell material approaches-1. This means that under the boundary condition of simple supports, a geometrically thick shell is mechanically equivalent to a thin or membrane shell, and therefore the use of membrane shell theory suffices even for a reasonably thick shell if the shell material is highly auxetic.