Your study really focuses on the shape that bolts take under load? In general, knowing the yield strength is more than enough for a screw calculation. In this case you could put the values you want for the Young's modulus and the Poisson ratio without influencing the result.
This is because in general a screw study is concerned with the moment when the screw loses its tightening function .
To simplify, the tightening torque of a screw is established so that the resulting force in the body of the screw corresponds to 80% of its yield strength. At this point, the screw is deformed according to its Young's modulus (elongation) and its poisson's ratio (shrinkage) but this deformation has no impact on the quality of the connection which depends on the force exerted by the screw.
Don't forget to put the tightening torque on the plan when it is important !