It is also pointed out that the nonlocal approach distorts the shape of the stress-strain diagram, which has to be taken into account when designing an appropriate local softening law. It has been shown that certain nonlocal formulations are inherently incapable of reproducing the entire material degradation process up to complete failure. Unless we are interested only in the response at the onset of localization, models that exhibit the special type of stress locking described in the paper should be avoided. Load-displacement diagrams of concrete specimens tested under direct tension typically exhibit a relatively steep drop immediately after the peak load, followed by a long tail. The shape of diagrams obtained with a nonlocal model using a linear local softening law are not at all realistic.
More reasonable response is produced by an exponential local softening law.
Due to its limited extent, the present study has dealt exclusively with damage-type models that unload to the origin. Another sound nonlocal approach can be developed in the context of plasticity. Comparison of nonlocal damage and plasticity theories and analysis of the structure and evolution of the process zone shall be presented in a separate paper. Please send me an email if you wish to receive the complete paper.