Default parameters in the stabilize argument in the step definition should be fine. If this is not working, then something else is wrong in your model.
I would think about the following questions: Is this a 2D/3D model? What are the loading/boundary conditions? Are there any warning nodes/elements? What do the .msg/.dat files say? When does the model fail (in the .sta file)?
I imagine you are more interested in joint motion since you are applying linear elasticity to ligaments; as you must know, ligaments are quite nonlinear. Linear elasticity will result in a stiff joint at
lower loads/deformations and, perhaps, not so stiff joint at
high loads/deformations. If you care about end-state loads/deformations of the joint at
moderate loads/deformations, then linear elasticity may work just fine. But if that is not the case, then you should look into hyperelastic (or rubber-like) material models, the simplest one being Neo-Hookean. Google search will get you the material parameters appropriate for ligaments. Ultimately, however, a more advanced model (like Weiss or Holzapfel) will be needed if you are interested in a more
accurate model of the ligament.
If you want to explain the goals and scope of the project, perhaps, I could suggest a few things. For example, are you interested in ligaments (fiber stress/strain) themselves or are you more interested in the motion of the joints? Which ligaments are you interested in? I am sure its a 3D application but are you interested in transient or equilibrium state behavior, i.e., dynamic vs. static analysis?
Note that the highlighted keywords are to emphasize the subjective nature of these terms. Your engineering skill will come in to play while defining these terms.