DISCRETIZATION INFLUENCE ON REGULARIZATION BY 2 LOCALIZATION LIMITERS

In materials With a Strain-softening characteristic behavior, classica l continuum mechanics favors uncontrolled strain localization in numer ical analyses. Several methods have been proposed to regularize the pr oblem. Two such localization limiters developed to overcome spurious i nstabilities in computational failure analysis are examined and compar ed. A disturbance analysis, on both models, is performed to obtain the closed-form solution of propagating wave velocities as well as the ve locities at which the energy travels. It also shows that in spite of f orcing the same stress-strain response, the wave equation does not yie ld similar results. Both propagations of waves are dispersive, but the internal length of each model is different when equivalent behavior i s desired. In fact, the previously suggested derivations of gradient m odels from nonlocal integral models were not completely rigorous. The perturbation analysis is pursued in the discrete space where computati ons are done. and the closed form solutions are also obtained. The fin ite-element discretization introduces an added dispersion associated t o the regularization technique. Therefore, the influence of the discre tization on the localization limiters can be evaluated. The element si ze must be smaller than the internal length of the models in order to obtain sufficient accuracy.