Finite plastic deformation of a circular membrane under hydrostatic pressure—I: Rate-independent behaviour

Abstract

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.