different coordinate for anisotropicmaterial in FEM simulation

I have a question which I don not understand. In the simulations of deforming of an anisotropic material like aluminum alloy sheet, different coordinates applied to the specimen model may leads to different results. But why? I mean for example, when the uniaxial tension specimen model is in rolling direction or in transverse direction, the anisotropic yield criterion is the same, the associated flow rule but why the results are different?