A general theory for nonlocal softening plasticity of integral-type

This paper deals with a comparison of several models, proposed in the literature, of softening plasticity with internal variables regularized by nonlocal averaging of integral type. The analyzed models of softening plasticity are divided in two groups. The former complies with models based on the principle of nonlocal maximum plastic dissipation; the latter is given by models formulated ad hoc without any recourse to thermodynamic requirements. In general, these models are not easy to compare. Actually, the formulations based on the principle of nonlocal maximum plastic dissipation appears to be quite different in terms of the free energy and of the yield function. On the other side, it is not trivial to check the thermodynamic admissibility of nonlocal models ad hoc formulated. To highlight the fundamental properties of these models in order to exploit the similarities and the differences between them, a general treatment of softening plasticity with internal variables is preliminarily proposed in the framework supplied by convex analysis and by the generalized standard material. It is shown that this framework provides the suitable tools to perform a theoretical analysis of such nonlocal problems. The proposed nonlocal formulation of softening plasticity combines in a quite general way the effect of local and nonlocal internal variables in the expressions of the free energy and of the elastic domain. As a consequence, several models of softening plasticity based either on thermodynamic considerations or on ad hoc formulations can be derived from the proposed model. The maximum dissipation principle is provided for each analyzed model.