The differences between the strain achieved in a Transient Structural vs a Static Structural are problem dependent. They could be big or small, but in this case, there is no data from Static Structural because there is no solution past the tip of the bump, so Transient is all you have.
There may be differences in strain when changing from a Linear Elastic material to a Hyperelastic material model. However you need to perform a suite of hyperelastic tests on the material and fit the model constants to the material data to get accurate predictions from the model.
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