Mechanica uses Large Deformation analysis for non-linear cases. I have not worked with this and cannot comment whether it is acceptable for "rubber" parts. Please see the below extract from a PTC technical paper.
Summary
In general, if the displacement is more than half of the thickness of the part, the option for large deformation should be used. For complicated models, this could be expensive in terms of time and disk space. A standard analysis without the option can be run initially to check the deformation values and a decision can be made on the need to run the analysis with the Large Deformation option.
At this point the Large Deformation option has the limitations listed below:
i) It can be used with static analysis only.
ii) Only 3D or 2D solid elements are supported with Large Deformation Analysis.
iii) Only models with isotropic material properties are allowed.
iv) No temperature dependent properties are allowed.
v) Loads have to be with respect to the WCS. No bearing loads or loads as function of coordinates are allowed. Loads should not be close to the buckling loads.
