Can anyone help me in listing out various fracture models for modeling concrete fracture using softwares like ABAQUS. I do also need various numerical models available for studying the fracture process of concrete mathematically. Thanks in advance.
Usually, smeared crack approach for modeling of the cracks is adopted. Within the smeared concept, two options are available for crack models: the fixed crack model and the rotated crack model.
If you want a continuum damage approach, you can use Mazar's model or one of its derivative. Reference: Mazars, J. (1986). A description of micro-and macroscale damage of concrete structures. Engineering Fracture Mechanics, 25(5), 729-737.
I suggest you Mazar's Continuum Concrete Damage. In Abaqus, you can try this constitutive model "mazar-model_umat.zip" (http://s.pudn.com/upload_log_en.asp?e=3932161).
Another bibliographi is "Continuum Damage Theory—Application to Concrete" (http://ascelibrary.org/doi/abs/10.1061/(ASCE)0733-9399(1989)115:2(345)).
Smeared crack model has the advantage to be easily implementation. But this kind of damage model can be use as a first approach. Despite that, continuous damage models as Mazars model are preferable.