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Thanks Ming.Â
My impression is that your model might be over-constrained compared to what happens in the actual compression experiment. Instead of using fixed support, try modeling the compression plates at the top and bottom then define contact pairs with appropriate friction coefficients (this is easier in Explicit Dynamics and Ansys LS-DYNA). Then try comparing your deformation pattern with that of the experiment.
You are right and compression response of some materials are different than tensile response. However, if you'd like to consider this effect, the tension-compression asymmetry of the materials should also be characterized experimentally. Â