This paper focuses on the numerical simulation of strain softening mechanical problems. Two problems arise: (1) the constitutive model has to be regular and (2) the numerical technique must be able to capture the two scales of the problem (the macroscopic geometrical representation and the microscopic behaviour in the localization bands). The Perzyna viscoplastic model is used in order to obtain a regularized softening model allowing to simulate strain 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 showing strain localization. As the key ingredient of the adaptive strategy, a residual-type error estimator is generalized to deal with such highly non-linear material model.
In several numerical examples the adaptive process is able to detect complex collapse modes that are not captured by a first, even if fine, mesh. Consequently, adaptive strategies are found to be essential to detect the collapse mechanism and to assess the optimal location of the elements in the mesh.