On the modeling of dissipative mechanisms in a ductile softening bar

The computational modeling of softening materials is still a challenging subject. An interesting way to deal with this problem is to adopt a variational framework. However, there are appealing features in using a classical approach. We explore the possibilities of both frameworks to include dissipative mechanisms. We start with a one-dimensional variational plastic-damage model rewritten in a classical framework, where regularization through viscoplasticity is applied. We highlight the appearance of an implicit internal length in the plastic strain field during the damage phase, allowing plasticity to evolve over a region before concentrating. Then, a consistent variational approach is adopted. A plastic strain gradient term is added to the global energy functional, with variable internal length coupled to the damage level. This model is further enriched by the addition of a hardening variable to the plastic evolution. A comparative analysis of the computational implementation of the different alternatives is performed.