The most relevant material models and/or material definitions available in Abaqus are:
Density: For any simulations that involves dynamics or body forces such as gravity, the density must be supplied.
Elastic - Linear elastic - Isotropic: Defined by the Young's modulus $E$ and the Poisson's ratio $\nu$.
Elastic - Linear elastic - Engineering Constants: Defined by the nine engineering constants for an orthotropic material, $E_1, E_2, E_3, \nu_{12}, \nu_{13}, \nu_{23}, G_{12}, G_{13}, G_{23}$
Elastic - Linear elastic - Lamina: Typically used for shells and layered shells. Includes the four engineering constants for plane stress, $E_1, E_2, \nu_{12}, G_{12}$, and additionally the shear moduli $G_{12}$ and $G_{13}$.
Elastic - Linear elastic - Orthotropic: Defined by the stiffness matrix components, as an alternative to using the Engineering Constants.
Expansion - Isotropic: The coefficient of linear thermal expansion $\alpha$.
Expansion - Orthotropic: The 3 coefficient of linear thermal expansion, $\alpha_1, \alpha_2, \alpha_3$.
Other models for material behaviors will be introduced for particular applications. These includes plasticity as well as failure and damage models for composites.
Several examples can be found in Abaqus Scripting.