Comparison of integral-type nonlocal plasticity models for strain-softening materials

The paper analyzes and compares a number of softening plasticity models regularized by nonlocal averaging. To highlight the fundamental properties and gain insight into the regularizing effect of various formulations, the localization problem is examined in the one-dimensional setting. It is shown that some of the theoretically appealing formulations are not genuine localization limiters, and that a localized plastic zone of nonzero measure is obtained only with softening laws that take into account the effect of both the local and the nonlocal cumulative plastic strain. The evolution of the plastic zone is studied, and formulations suitable for the description of the entire deformation process up to the complete loss of cohesion are identified. The effect of boundaries on the shape of the plastic strain profile and on the dissipated energy is analyzed. Attention is also paid to the thermodynamic aspects of nonlocal plasticity, especially to the consistent extension of the concept of generalized standard materials to nonlocal continua.