Since your displacement is 33% of expected, you are overpredicting the stiffness. Assuming your load is correct, it is either the material model, the geometry or the boundary constraints. You mentioned that you are using a Mooney Rivlin model, but you did not say how many terms? Perhaps your material model needs more terms to account for an important inflection point in the stress-strain history at higher strains. Maybe you are overpredicting the stiffness at higher strains.
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