You can define tension or compression damage (dt and dc respectively) with the concrete damaged plasticity (CDP) model for concrete in Abaqus.
For the tensile damage dt you have to enter it in Abaqus/CAE using the following steps: Property module: material editor: Mechanical Plasticity Concrete Damaged Plasticity: Tensile Behavior: Suboptions Tension Damage: Type: Strain or Displacement
For the compressive damage dc you have to enter it in Abaqus/CAE using the following steps: Property module: material editor: Mechanical Plasticity Concrete Damaged Plasticity: Compressive Behavior: Suboptions Compression Damage
Please refer to Section 23.6.3 of the Abaqus Analysis User's Manual for more details.