Configurational stress, yield and flow in rate–independent plasticity

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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 Levy–von Mises theory is obtained.