Plastic Stability of Spherical Shells

Incipient axisymmetric plastic buckling of complete spherical shells subjected to external hydrostatic pressure is studied by the use of rate equations. Buckling is initiated under increasing pressure with the rate of pressure increase determined by forcing the loading criterion of the J₂ incremental theory of plasticity to be satisfied everywhere in the shell. Forcing the loading criterion to be satisfied removes the multiplicative constant indeterminacy in the buckling velocity field. The incipient results suggest that the maximum pressure which would be obtained from stepwise following of the entire load-deformation history is not significantly greater than the tangent modulus pressure required for first bifurcation.