On the effect of the Poisson's ratio (positive and negative) on the stability of pressure vessel heads

Materials with negative Poisson's ratio (auxetic) exhibit an unusual property of expanding when stretched in the direction normal to an applied uniaxial tension and vice versa when compressed, a phenomenon which is known to result in many beneficial effects in the performance of materials in various practical situations. In particular, it has long been suggested that spherical shells made from isotropic materials having Poisson's ratio less than −0.5 exhibit enhanced resistance to buckling as a result of externally applied normal pressure. This work uses finite elements (FEs) modelling to assess the behaviour of various spherical, torispherical and ellipsoidal shells when they are subjected to external (in all cases) or internal (in the case of torispherical and ellipsoidal shells) pressures. We find that to a first approximation, the critical buckling pressures scale linearly with (1 − ν 2 ) −1/2 thus suggesting that the critical buckling pressures tends to infinity as ν tends to −1, this being in accordance to what was known for spherical shells. We also find that the Poisson's ratio has an effect on the amplitude and the number of buckling wavelengths that occur when the shells buckle.