Finite plastic deformation of a circular membrane under hydrostatic pressure—II : Strain-rate effects

The large strain behaviour of a circular membrane under uniform hydrostatic pressure is examined for materials with transversely isotropic plastic properties. Time-independent material response is assumed, and both flow theory and deformation theory of plasticity are considered.A variational principle is first applied to derive the governing equations for the pressurized membrane. It is shown that a special solution previously given by Hill[7] for isotropic materials can readily be extended to certain transversely isotropic membranes.A finite element solution based on Hill's extremum principle[24] is then developed to study the influence of anisotropy on the finite deformation behaviour of the membrane. Conditions where localized-necking bifurcations become possible are also discussed.