as you are using shell elements, the material orientation x-axis (= E1) is by definition always in the local XY plane of the shells. In your case, you might need to consider a Solid Element model, to have a local E1 orientation in parallel to the z-axis. The material law would then be MAT9 or MAT9ORT.
I have CTETRA elements in my model, so I think I have to use MAT9ORT associated to PSOLID property. I do not have properties of each layer because my material has not proper layers. I have mechanical properties about the whole body obtained throughout tensile tests.
My doubt is if the directions 1, 2 and 3 along which I have to define mechanical properties in MAT9ORT (as elastic modulus, Poisson's ratio etc.) are about local reference system of each element, or are about the global reference system xyz. And I do not understand how can I check direction 1, 2 and 3 in my model.