Variational principles for softening gradient dependent plasticity

A gradient dependent plasticity model is analysed in which the yield function not only depends on the stress tensor and an invariant plastic strain measure, but also on the spatial derivatives of the latter quantity. A minimum variational principle is obtained by analysing the structure discretized into sufficiently small plastic elements and thus the uniqueness of FE solutions can be ensured for softening plasticity. The positive definiteness of the variational functional is determined only by the sign of the diffuse coeffiecient associated with the highest order derivative of the plastic multiplier in the yield function. In order to adopt mix/hybrid elements, several general variational principles are obtained by relaxing the associated constraints on the displacements-strain-stress and/or plastic multiplier-gradient-radiation fields.