Where did you get your constants from? Literature? Or, did you fit your material law to some experimental data? Try the material constants on a homogeneous uniaxial deformation on 1 element.
This is going to be a lot more than you are looking for but this subject interests me and I hope this gives you some background:
Ideally, if one wishes to have complete understanding of this business, one should write a symbolic math script and do a nonlinear curve fitting to get their material constants, verify Abaqus results against the results from the script, and only then go to the next step. It is known that for bounds have to be set on the material constants for the material to be physically reasonable (due to inequalities such as Coleman-Noll and Baker-Ericksen). Baker-Ericksen does not hold for anisotropic materials. The downside of Coleman-Noll inequality is that it is unreasonable under large deformation but this is the best commercial codes will offer, if at all.
Additionally, using the deformation gradient for a simple deformation, check if the elasticity tensor (C_ijkl) is positive definite (i.e., the energy is a bowl in 3D Euclidean space), full rank (rows/columns are linearly independent), and well-conditioned (condition number should not be too high) over the entire range of deformation. You may then try to impose non-trivial deformations and see how the model is doing. All of this may be done in a symbolic math script.
If the simulation in an FE solver still gives issues, then the problem *may* have to do with the implementation. And, if that is the concern, you can always try to use some other code (freely available or otherwise).
If you are interested in this subject, you may wish to look up Neff and Schroeder's (relatively) work on polyconvex strain energy density functions.
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