Configurational stress, yield and flow in rate-independent plasticity

The role of configurational stress in yield and plastic flow is discussed for a macroscopic model of rate-independent, finite-strain plasticity. The model is based on the traditional elastic-plastic decomposition of the deformation gradient, on integral balance laws and on thermodynamically restricted, rate-independent constitutive relations. Its formulation emphasizes the intermediate configuration in both the development of constitutive relations and the expression of balance laws. In addition to the usual balance laws, a couple balance is included to represent the action of plastic couples in the intermediate configuration. In particular, it is shown that the internal couple decomposes into a non-dissipative configurational stress and a dissipative couple that resists plastic flow. The couple balance thus determines a relation between the configurational stress and the plastic-flow resistance, a relation that can be interpreted as a generalized yield condition. A dissipation function is introduced and a maximum-dissipation criterion is used to obtain additional constitutive restrictions, which lead to a counterpart in the intermediate configuration of the classical normality conditions. The versatility of the framework is illustrated by applying it to rigid-plastic flow, in which case a nonlinear generalization of the classical Lévy-von Mises theory is obtained.