I was conducting a FEA analysis of a symmetric isotropic structure under a loading condition. I will not mention the material I was using. Under that loading, one part of the structure was in tension and other in compression. When I reversed the loading condition, the part that was in compression previously was now in tension and vice versa. However, the displacements and the Von-Mises stresses that were seen on the part of the structure that was in tension in the initial loading condition, and again which was in tension in the reversed loading condition, I saw a difference in it and I couldn't understand why it was happening. So I thought maybe it is possible for the material to have different elastic modulus and Poisson's ratio under compression and tension. Is this true? If yes, then in most of the FEA softwares, there is option to add only one elastic modulus. Why is that? Is there any specific class of materials where this happens, or we have to conduct experiments to individually check each and every material if their elastic modulus is the same of different under tension and compression?
For small strains of stable materials, the tensile and compressive elastic moduli are equal. This is equivalent to saying that a smooth energy minimum looks like a (symmetric) parabola up close; an energy well in the shape of a parabola characterizes an ideal spring with equal elongation and contraction spring constants.
This approximation works well for metals, ceramics, and crosslinked polymers, for example, whose elastic strain is small (1%, say). This is why you have the option to enter only one Young's modulus, for example. However, the approximation typically does not work for large elastic strains of hyperelastic materials such as elastomers, which may stretch their own length (100% strain) and much more. As shown below (source), the stress–strain slopes are visually identical for slight positive and negative strains but differ for larger strains.
Since the same argument holds for the bulk and shear modulus, it must hold for Poisson's ratio, which is not independent if Young's modulus and either the bulk or shear modulus are specified.