What kind of material do you want to analyze ? ANSYS has cast iron material model which allows you to define the data from compressive and tensile stress-strain curves separately.

To analyze Cast Iron, under the load, when stresses are in the elastic range, stress -strain curves in tension and compression is the only option?
Cast Iron Young Modulus is also different in Tension and Compression, these values are easy to get for different types of cast iron as compare to Stress Strain curves.
Is there a way to do the elastic analysis with tow different E values (for Tension and Compression) only?

It is a plastic model and that is how it should be used, so I do not recommend the following . But if you have to and you are confident that this is OK, Try setting yield to something very high, say 10000mpa for tension and 20000mpa for compression, so it does not yield. I never done this so make sure you double check your results. So be careful if this is used, for proper calculation. I would send ansys support also an email to check if it can be used like this, because I have not much experience with this model.

I’m afraid you can’t define different Young’s modulus for tension and compression separately. However, since you are interested in linear elasticity, maybe you could use the two Young’s moduli to create linear portions of both stress-strain curves (for tension and compression). Then you would have to take one or two points from each curve and put them into ANSYS material definition. But since cast iron is plasticity model, you would have to use some nonlinear elastic model where you can provide stress-strain curve data as input to do this trick.

You cannot have different E values in tensio compression in cast iron, have that in mind, but if you need them to be elastic see my previous post.

So it needs to be used with MP,EX command so if we try to be clever and set different compression stress strain data that would be a larger E mod, than tension and as set MP, then here is what we get, so not possible:

*** ERROR ***
For material 1 at temperature 20, the initial slope (4.E+11) of the
stress-strain curve based on the TB,UNIAXIAL table with option (COMP)
is greater than EX (2.E+11).