Hi Jay,

Regarding few of your many questions đź™‚ :

For what you want to model, poroelastic material fits the best, IMO. That means a solid matrix fully or partially saturated with fluid.

The solid matrix material can be elastic or hyperelastic. That depends fully on what you want to model and properties of your specimen. I would use hyperelastic in case large deformations are intended.

I have never used porous elastic material. So, I can not help you with that.

To consider the effect of fluid phase of your poroelastic material, you HAVE to use Soils, and cant use standard static analysis. This will let you to consider the time-dependency of the response of your material which is otherwise absent in normal static procedure.

For the units of k, it is true that they use different units in articles based on their field and also in Abaqus. You should make sure to use the correct dimension. If I remember correctly, Abaqus uses dimension of speed for k, LT-1. When I was working on this topic some years ago, I remember that I eventually found a way to convert the k values from articles to this dimension to be usable in Abaqus. But, I just cant recall now.

To define a tissue under static/quasi static loading, you should define the properties of the solid matrix (elastic or hyperelastic moduli as well as the Poissons ratio or its equivalent in hyperelasticity), void ratio (I think it was the ratio of the fluid content to the solid matrix, not sure though) and the permeability of the matrix to the fluid.

I believe if you refer to Abaqus User Manual on permeability topic, you will find your answer on dimensions, parameters and much more.

Hope this was a help.