An incrementally continuous deformation theory of plasticity with unloading

For predictions of plastic buckling, and especially postbuckling behaviour and imperfection sensitivity it is desirable to have a plasticity theory that combines some of the desired characteristics of both the ¯ow and deformation theories of plasticity. For this purpose a way to include unloading within a deformation theory of plasticity is given that preserves the incremental continuity of the resulting constitutive equations. This can only be achieved by allowing plastic deformations to occur within the yield surface. Such plastic deformations are controlled by a parameter m, which describes how rapidly the possibility of such plastic deformations disappears as the stress state moves away from the yield surface. A ®nite strain version of the formulation is given. The approach can be implemented with minimal changes to an elastic predictor ± radial return algorithm for the ¯ow theory of plasticity, by changing the elastic predictor phase only. For tests involving thick-walled …D=t110† cylinders with known axisymmetric imperfections under axial compression, this new deformation theory overpredicted the concertina wrinkling type deformations for a given amount of applied axial shortening, whereas the ¯ow theory underpredicted these wrinkling deformations in some cases.