Hardening plasticity with nonlocal strain damage

In this paper a thermodynamically consistent theory of elastoplasticity coupled with nonlocal damage in the strain space is presented. The theory is developed in the framework of the generalized standard material and the constitutive model is identified by the specification of the dissipation and of the internal energy depending on total and plastic strain, kinematic internal variables, nonlocal relaxation stress and entropy. Coupling between plasticity and nonlocal damage is achieved by using a plastic-damage dissipation which can be split in two parts. One damage dissipation occurs independent of plastic behavior while the other one is coupled with plasticity. The former dissipation occurs in both the elastic and plastic behaviors. Further the local uniqueness conditions of the considered model are studied. The structural model is then addressed and variational formulations with different combinations of local and nonlocal state variables are provided. Finally the general model governed by a single dissipation is specialized to a simplified model which is defined by two dissipations which are, in turn, equivalent to define a yield function and a nonlocal damage loading function. Two examples of the application of the theory are then provided in which no mesh dependence is apparent.