There are a few models that are implemented in Abaqus (see manual), but i think that the Concrete Damaged Plasticity (CDP) model is the most popular one.
It can be used both in Abaqus/Standard and Abaqus/Explicit.
It is based on the two surface Lubliner's Yield criterion and it introduces the elastic degradation both in tension and compression.
Maby You will find these publications useful (especially the first one):