Choosing Incompressibility Parameters

How do you pick the value of incompressibility parameter D when we want to add a small amount of compressibility to the hyperelastic material?

The incompressibility parameter D is nothing but 2/(initial bulk modulus). If you wish to add a small amount of incompressibility (large but finite bulk modulus), then you should add a small value for D. Note that the parameter D has the units of 1/stress. So, if the initial shear modulus of the material is 2.5 MPa, then a value of 1e-2 MPa^-1 would be a reasonable value for D.