Adaptivity based on error estimation for viscoplastic softening materials

This paper focuses on the numerical simulation of strain softening mechanic al problems. Two problems arise: (1) the constitutive model has to be regul ar and (2) the numerical technique must be able to capture the two scales o f the problem(the macroscopic geometrical representation and the microscopi c behaviour in the localization bands). The Perzyna viscoplastic model is u sed in order to obtain a regularized softening model allowing to simulate s train localization phenomena. This model is applied to quasistatic examples . The viscous regularization of quasistatic processes is also discussed: in quasistatics, the internal length associated with the obtained band width is no longer only a function of the material parameters but also depends on the boundary value problem (geometry and loads, specially loading velocity ). An adaptive computation is applied to softening viscoplastic materials show ing strain localization. As the key ingredient of the adaptive strategy, a residual-type error estimator is generalized to deal with such highly non-l inear material model. In several numerical examples the adaptive process is able to detect comple x collapse modes that are not captured by a first, even if fine, mesh. Cons equently, adaptive strategies are found to be essential to detect the colla pse mechanism and to assess the optimal location of the elements in the mes h. Copyright (C) 2000 John Wiley & Sons, Ltd.