Buckling of viscoelastic spherical shells

Viscoelastic spherical shells exhibit a wide range of time/rate-dependent buckling behaviors when subjected to pressure. For certain loadings, buckling can even occur after a significant time delay, termed creep buckling. To gain a thorough understanding of the nonlinear time-dependent buckling behavior of viscoelastic spherical shells, this work develops an analytical model employing the small-strain, moderate-rotation shell theory combined with a linearly viscoelastic material law. Numerical results are presented for axisymmetric spherical shells with geometric imperfections for two types of loading: a prescribed rate of volume change and a prescribed pressure that remains constant after it is applied. The first type reveals the rate-dependent behavior of viscoelastic buckling while the constant pressure loading is used to quantify creep buckling phenomena. The results show that viscoelasticity and loading rates play important roles in the load-carrying behavior of these shells, and the results for the constant pressure loading reveal an unexpected and important connection between the short-time elastic buckling limit and the long-time creep buckling limit. An imperfection sensitivity map is constructed for the constant pressure loading showing three regimes with qualitatively different behaviors: near-instantaneous buckling, creep buckling and no buckling.